Question 1

A cylindrical tank with a hemispherical bottom has a total height of 5 m and a diameter of 4 m. Calculate the total surface area of the tank. (Take $\pi = 3.14$)

Accepted Answer

Correct Option: B. Solution: The total surface area includes the curved surface area of the cylinder and the curved surface area of the hemisphere. Radius $r = 2$ m. Height of the cylinder $h = 5 - 2 = 3$ m. CSA of cylinder = $2\pi rh = 2 	imes 3.14 	imes 2 	imes 3 = 37.68$ m². CSA of hemisphere = $2\pi r^2 = 2 	imes 3.14 	imes 2^2 = 25.12$ m². Total surface area = $37.68 + 25.12 = 117.76$ m².

Question 2

A cylindrical tank has a hemispherical depression at one end. If the height of the cylinder is $h$ and the radius of both the cylinder and hemisphere is $r$, what is the total surface area of this structure?

Accepted Answer

Correct Option: A. Solution: The total surface area is the sum of the curved surface area of the cylinder ($2\pi rh$) and the curved surface area of the hemisphere ($2\pi r^2$).

Question 3

What is the total surface area of a solid formed by a cylinder with two hemispheres attached at its ends?

Accepted Answer

Correct Option: A. Solution: The total surface area of the solid is the sum of the curved surface areas of the cylinder and the two hemispheres.

Question 4

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14 	ext{ cm}$ and the total height of the vessel is $13 	ext{ cm}$. Find the inner surface area of the vessel.

Accepted Answer

Correct Option: B. Solution: The inner surface area of the vessel is the sum of the curved surface area of the hemisphere and the curved surface area of the cylinder. The radius $r$ is $7 	ext{ cm}$. Thus, the inner surface area is $2\pi r^2 + 2\pi rh = 2\pi 	imes 7^2 + 2\pi 	imes 7 	imes 6 = 462 + 154 = 616 	ext{ cm}^2$.

Question 5

A composite solid is formed by joining a hemisphere and a cone, both having the same base radius of 4 cm. If the height of the cone is 6 cm, find the total surface area of the solid. (Take $\pi = 3.14$)

Accepted Answer

Correct Option: C. Solution: The total surface area of the solid is the sum of the curved surface area of the hemisphere and the cone. CSA of hemisphere = $2\pi r^2 = 2 	imes 3.14 	imes 4^2 = 100.48$ cm². CSA of cone = $\pi rl = 3.14 	imes 4 	imes \sqrt{4^2 + 6^2} = 75.36$ cm². Total surface area = $100.48 + 75.36 = 175.84$ cm².

Question 6

A decorative block is made of a cube with a hemisphere on top. If the edge of the cube is 5 cm and the diameter of the hemisphere is 4.2 cm, what is the total surface area of the block?

Accepted Answer

Correct Option: B. Solution: The total surface area of the block is the surface area of the cube minus the base area of the hemisphere plus the curved surface area of the hemisphere.

Question 7

A medicine capsule is in the shape of a cylinder with two hemispheres attached at its ends. If the length of the capsule is 14 mm and the diameter is 5 mm, what is the surface area of the capsule?

Accepted Answer

Correct Option: A. Solution: The surface area of the capsule is the sum of the curved surface area of the cylinder and the curved surface areas of the two hemispheres.

Question 8

A cylindrical tank has a height of 1.45 m and a radius of 30 cm. A hemispherical depression is made at one end. What is the total surface area of the tank?

Accepted Answer

Correct Option: A. Solution: The total surface area of the tank is the sum of the curved surface area of the cylinder and the curved surface area of the hemisphere. CSA of cylinder = $2\pi rh = 2\pi (0.3)(1.45) = 2.73\pi$ m². CSA of hemisphere = $2\pi r^2 = 2\pi (0.3)^2 = 0.18\pi$ m². Total surface area = $2.73\pi + 0.18\pi = 2.91\pi$ m², which is approximately 3.3 m².

Question 9

A decorative block is made of a cube with edge length 5 cm and a hemisphere with a diameter of 4.2 cm placed on top. Calculate the total surface area of the block, excluding the base of the hemisphere.

Accepted Answer

Correct Option: A. Solution: The surface area of the block is calculated by adding the total surface area of the cube and the curved surface area of the hemisphere, excluding the base area of the hemisphere: $150 + 2 \pi (2.1)^2 = 163.86 	ext{ cm}^2$.

Question 10

What is the formula for the curved surface area (CSA) of a cylinder with radius $r$ and height $h$?

Accepted Answer

Correct Option: B. Solution: The curved surface area of a cylinder is given by $2\pi rh$, where $r$ is the radius and $h$ is the height.

Question 11

A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the entire rocket is $26 	ext{ cm}$, while the height of the conical part is $6 	ext{ cm}$. The base of the conical portion has a diameter of $5 	ext{ cm}$, while the base diameter of the cylindrical portion is $3 	ext{ cm}$. Calculate the area of the rocket painted with orange if only the conical part is painted.

Accepted Answer

Correct Option: A. Solution: The area to be painted orange is the curved surface area of the cone plus the base area of the cone minus the base area of the cylinder. $\pi rl + \pi r^2 - \pi (r')^2 = \pi[(2.5 	imes 6.5) + (2.5)^2 - (1.5)^2] = 63.585 	ext{ cm}^2$.

Question 12

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. What is the volume of the toy?

Accepted Answer

Correct Option: A. Solution: The volume of the toy is the sum of the volume of the hemisphere and the volume of the cone, which is $25.12 	ext{ cm}^3$.

Question 13

A medicine capsule is in the shape of a cylinder with two hemispheres attached at each end. If the total length of the capsule is 14 mm and the diameter is 5 mm, what is the total surface area of the capsule?

Accepted Answer

Correct Option: A. Solution: The total surface area of the capsule is the sum of the curved surface area of the cylinder and the curved surface areas of the two hemispheres: $2\pi rh + 2 	imes 2\pi r^2 = 2\pi 	imes 2.5 	imes 4 + 4\pi 	imes (2.5)^2 = 220 	ext{ mm}^2$.

Question 14

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8g mass.

Accepted Answer

Correct Option: B. Solution: Calculate the volume of each cylinder and multiply by the density of iron to find the mass.

Question 15

A medicine capsule is in the shape of a cylinder with two hemispherical ends. The length of the entire capsule is 14 mm and the diameter is 5 mm. Find its surface area. (Take $\pi = \frac{22}{7}$)

Accepted Answer

Correct Option: B. Solution: The surface area of the capsule is the sum of the curved surface area of the cylinder and the surface area of the two hemispheres: $2\pi rh + 2\pi r^2$. Here, $r = 2.5 	ext{ mm}$ and $h = 14 - 2 	imes 2.5 = 9 	ext{ mm}$. Substituting the values, we get $2 	imes \frac{22}{7} 	imes 2.5 	imes 9 + 2 	imes \frac{22}{7} 	imes (2.5)^2 = 234 	ext{ mm}^2$.

Question 16

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Accepted Answer

Correct Option: B. Solution: The inner surface area is the sum of the curved surface area of the hemisphere and the curved surface area of the cylinder.

Question 17

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Accepted Answer

Correct Option: A. Solution: The total surface area of the toy is the sum of the curved surface area (CSA) of the hemisphere and the CSA of the cone.

Question 18

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top is 5 cm. It is filled with water up to the brim. When lead shots, each a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped. (Take $\pi = 3.14$)

Accepted Answer

Correct Option: B. Solution: The volume of the cone is $\frac{1}{3} \pi r^2 h = \frac{1}{3} 	imes 3.14 	imes (5)^2 	imes 8 = 209.33 	ext{ cm}^3$. One-fourth of this volume is $\frac{209.33}{4} = 52.33 	ext{ cm}^3$. The volume of one lead shot is $\frac{4}{3} \pi (0.5)^3 = 0.524 	ext{ cm}^3$. Therefore, the number of lead shots is $\frac{52.33}{0.524} \approx 100$.

Question 19

A vessel is shaped like a cylinder with two hemispherical ends. The length of the vessel is 14 cm and the diameter is 5 cm. What is the total surface area of the vessel? (Use $\pi = 3.14$)

Accepted Answer

Correct Option: A. Solution: The total surface area is the sum of the curved surface area of the cylinder and the two hemispheres: $2\pi rh + 4\pi r^2 = 2 	imes 3.14 	imes 2.5 	imes 9 + 4 	imes 3.14 	imes 2.5^2 = 282.6$ cm².

Question 20

A toy is made by combining a hemisphere and a cone. If the radius of the base of the cone and the hemisphere is $r$, and the slant height of the cone is $l$, what is the total surface area of the toy?

Accepted Answer

Correct Option: A. Solution: The total surface area of the toy is the sum of the curved surface area of the hemisphere ($2\pi r^2$) and the curved surface area of the cone ($\pi rl$).

Question 21

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, surmounted by another cylinder of height 60 cm and radius 8 cm. Calculate the mass of the pole, given that 1 cm³ of iron has approximately 8g mass.

Accepted Answer

Correct Option: B. Solution: The volume of the first cylinder is $\pi r^2 h = \pi (12)^2 	imes 220$. The volume of the second cylinder is $\pi (8)^2 	imes 60$. The total mass is $8 	imes (\pi (12)^2 	imes 220 + \pi (8)^2 	imes 60) = 160 	ext{ kg}$.

Question 22

A toy is made by placing a cone of height 6 cm on a hemisphere with a radius of 3 cm. If the slant height of the cone is 6.5 cm, what is the total surface area of the toy? (Use $\pi = 3.14$)

Accepted Answer

Correct Option: C. Solution: The total surface area is the sum of the curved surface area of the cone and the hemisphere: $\pi rl + 2\pi r^2 = 3.14 	imes 3 	imes 6.5 + 2 	imes 3.14 	imes 3^2 = 150.72$ cm².

Question 23

A medicine capsule is in the shape of a cylinder with two hemispheres attached at each end. The total length of the capsule is 14 mm and the diameter is 5 mm. What is the surface area of the capsule? (Use $\pi = 3.14$)

Accepted Answer

Correct Option: B. Solution: The capsule consists of a cylindrical part and two hemispherical ends. The radius $r = 2.5$ mm and the height of the cylinder $h = 14 - 2 	imes 2.5 = 9$ mm. Surface area of the cylinder = $2 \pi r h = 2 	imes 3.14 	imes 2.5 	imes 9 = 141.3$ mm². Surface area of two hemispheres = $2 	imes 2 \pi r^2 = 2 	imes 2 	imes 3.14 	imes 2.5^2 = 78.5$ mm². Total surface area = $141.3 + 78.5 = 219.8$ mm², approximately 220 mm².

Question 24

A tent is in the shape of a cylinder surmounted by a conical top. The height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m. Calculate the total area of the canvas used for making the tent.

Accepted Answer

Correct Option: A. Solution: The area of the canvas is the sum of the curved surface area of the cylinder and the curved surface area of the cone: $2\pi rh + \pi rl = 2\pi 	imes 2 	imes 2.1 + \pi 	imes 2 	imes 2.8 = 66.32 	ext{ m}^2$.

Question 25

A toy is made by combining a hemisphere and a cone with equal radii. If the radius of both the hemisphere and the cone is 3 cm, and the height of the cone is 4 cm, what is the total surface area of the toy?

Accepted Answer

Correct Option: C. Solution: The total surface area of the toy is the sum of the curved surface area of the hemisphere and the curved surface area of the cone. CSA of hemisphere = $2\pi r^2 = 2\pi (3)^2 = 18\pi$ cm². CSA of cone = $\pi r l = \pi (3) \sqrt{3^2 + 4^2} = 15\pi$ cm². Total surface area = $18\pi + 15\pi = 33\pi$ cm².

Question 26

A toy is made by mounting a cone on a hemisphere. If the radius of both the cone and hemisphere is 2 cm and the height of the cone is 2 cm, what is the total surface area of the toy? (Take $\pi = 3.14$)

Accepted Answer

Correct Option: A. Solution: The total surface area of the toy is the sum of the curved surface area of the hemisphere and the curved surface area of the cone. CSA of hemisphere = $2\pi r^2$ and CSA of cone = $\pi r l$, where $l = \sqrt{r^2 + h^2}$. Substituting $r = 2$ cm and $h = 2$ cm, $l = \sqrt{4 + 4} = \sqrt{8} = 2.83$ cm. Therefore, the total surface area is $2 	imes 3.14 	imes 2^2 + 3.14 	imes 2 	imes 2.83 = 37.68$ cm².

Question 27

A wooden toy is in the form of a cone mounted on a hemisphere. The radius of the hemisphere and the base of the cone is 2 cm, and the height of the cone is 2 cm. Calculate the volume of the toy. (Take $\pi = 3.14$)

Accepted Answer

Correct Option: D. Solution: The volume of the toy is the sum of the volumes of the hemisphere and the cone: $\frac{2}{3} \pi r^3 + \frac{1}{3} \pi r^2 h$. Substituting the values, we get $\frac{2}{3} 	imes 3.14 	imes (2)^3 + \frac{1}{3} 	imes 3.14 	imes (2)^2 	imes 2 = 25.12 	ext{ cm}^3$.

Question 28

A cylindrical tank with a hemispherical top is filled with water. The height of the cylindrical part is 1.45 m and the radius is 30 cm. Calculate the total surface area of the tank excluding the base. (Take $\pi = \frac{22}{7}$)

Accepted Answer

Correct Option: A. Solution: The total surface area of the tank is the sum of the curved surface area of the cylinder and the curved surface area of the hemisphere: $2\pi rh + 2\pi r^2$. Substituting the values, we get $2 	imes \frac{22}{7} 	imes 0.3 	imes 1.45 + 2 	imes \frac{22}{7} 	imes (0.3)^2 = 3.3 	ext{ m}^2$.

Question 29

A decorative block is made of a cube with an edge of 5 cm and a hemisphere with a diameter of 4.2 cm placed on top. What is the total surface area of the block? (Take $\pi = \frac{22}{7}$)

Accepted Answer

Correct Option: A. Solution: The total surface area of the block is the surface area of the cube minus the base area of the hemisphere plus the curved surface area of the hemisphere. TSA of cube = $6 	imes (5)^2 = 150$ cm². Base area of hemisphere = $\pi r^2$ where $r = 2.1$ cm. CSA of hemisphere = $2\pi r^2$. Therefore, the surface area of the block is $150 - \pi (2.1)^2 + 2\pi (2.1)^2 = 163.86$ cm².

Question 30

A wooden toy rocket is in the shape of a cone mounted on a cylinder. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. Find the area of the rocket painted with orange if the conical portion is painted orange.

Accepted Answer

Correct Option: A. Solution: The area to be painted orange is the CSA of the cone plus the base area of the cone minus the base area of the cylinder.

Question 31

A solid toy is in the shape of a hemisphere surmounted by a cone. The height of the cone is 3 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, what is the difference in volume between the cylinder and the toy? (Take $\pi = 3.14$)

Accepted Answer

Correct Option: B. Solution: The volume of the toy is the sum of the volumes of the hemisphere and the cone. Volume of hemisphere = $\frac{2}{3} \pi r^3$ and volume of cone = $\frac{1}{3} \pi r^2 h$. The radius $r = 2$ cm. Volume of toy = $\frac{2}{3} 	imes 3.14 	imes 2^3 + \frac{1}{3} 	imes 3.14 	imes 2^2 	imes 3 = 25.12$ cm³. The cylinder has a radius of 2 cm and height of 5 cm. Volume of cylinder = $\pi r^2 h = 3.14 	imes 2^2 	imes 5 = 62.8$ cm³. The difference in volume is $62.8 - 25.12 = 37.68$ cm³.

Question 32

A toy is made by combining a hemisphere and a cone. If the radius of the hemisphere is equal to the base radius of the cone, how do you calculate the total surface area of the toy?

Accepted Answer

Correct Option: A. Solution: The total surface area is the sum of the curved surface areas of the hemisphere and the cone.

Question 33

A cylindrical tank with a height of 1.45 m and a radius of 30 cm has a hemispherical depression at one end. What is the total surface area of the tank? (Use $\pi = \frac{22}{7}$)

Accepted Answer

Correct Option: B. Solution: The total surface area is the sum of the curved surface area of the cylinder and the curved surface area of the hemisphere: $2\pi rh + 2\pi r^2 = 2 	imes \frac{22}{7} 	imes 0.3 	imes 1.45 + 2 	imes \frac{22}{7} 	imes 0.3^2 = 3.3$ m².

Question 34

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Accepted Answer

Correct Option: A. Solution: The volume of the solid is the sum of the volumes of the cone and the hemisphere. Volume of cone = $\frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (1)^2 (1) = \frac{1}{3}\pi$ cm³. Volume of hemisphere = $\frac{2}{3}\pi r^3 = \frac{2}{3}\pi (1)^3 = \frac{2}{3}\pi$ cm³. Total volume = $\frac{1}{3}\pi + \frac{2}{3}\pi = \frac{5}{3}\pi$ cm³.

Question 35

A solid is formed by joining a cylinder with a height of 10 cm and radius 3 cm, and a hemisphere with the same radius on top of the cylinder. What is the total volume of the solid? (Use $\pi = 3.14$)

Accepted Answer

Correct Option: B. Solution: The volume of the cylinder is $\pi r^2 h = 3.14 	imes 3^2 	imes 10 = 282.6$ cm³. The volume of the hemisphere is $\frac{2}{3} \pi r^3 = \frac{2}{3} 	imes 3.14 	imes 3^3 = 56.52$ cm³. Total volume = $282.6 + 56.52 = 339.12$ cm³.

Question 36

A solid consisting of a right circular cone of height 120 cm and radius 60 cm stands on a hemisphere of radius 60 cm. It is placed upright in a right circular cylinder full of water such that it touches the bottom. What is the volume of water left in the cylinder if the radius of the cylinder is 60 cm and its height is 180 cm?

Accepted Answer

Correct Option: C. Solution: The volume of water left is calculated by subtracting the volume of the solid from the total volume of the cylinder. Correct calculation gives 30000 cm³.

Question 37

The volume of a composite solid formed by combining two basic solids is the sum of the volumes of the individual solids without any adjustment for overlapping.

Accepted Answer

Answer: True. Solution: When calculating the volume of composite solids, the total volume is the sum of the individual volumes of the constituent solids, as there is no overlap in volume.

Question 38

The total surface area of a composite solid consisting of a cylinder with two hemispheres at its ends is the sum of the curved surface areas of the cylinder and the two hemispheres.

Accepted Answer

Answer: True. Solution: The total surface area of such a composite solid is calculated by summing the curved surface areas of the cylinder and the two hemispheres, as the flat ends are not exposed.

Question 39

The actual capacity of a glass with a hemispherical depression at the bottom is less than its apparent capacity.

Accepted Answer

Answer: True. Solution: The actual capacity of the glass is reduced by the volume of the hemispherical depression, making it less than the apparent capacity.

Question 40

The total surface area of a composite solid is always the sum of the total surface areas of its individual components.

Accepted Answer

Answer: False. Solution: When calculating the surface area of a composite solid, overlapping areas are not counted twice. Therefore, the total surface area is not simply the sum of the total surface areas of the individual components.

Question 41

To find the surface area of a composite solid, you simply add the surface areas of all individual components.

Accepted Answer

Answer: False. Solution: The surface area of a composite solid is not the simple sum of the surface areas of its components because some areas may overlap or be hidden.

Question 42

When calculating the total surface area of a toy formed by a hemisphere and a cone, the base area of the hemisphere is included in the calculation.

Accepted Answer

Answer: False. Solution: The base area of the hemisphere is not included in the calculation of the total surface area, as it is not exposed when the hemisphere and cone are joined.

Question 43

The volume of a composite solid is not the sum of the volumes of its individual components.

Accepted Answer

Answer: False. Solution: The volume of a composite solid is indeed the sum of the volumes of its individual components, as no volume is lost when combining solids.

Question 44

The total surface area of a solid formed by a cylinder with two hemispheres at its ends is the sum of the curved surface areas of the cylinder and the two hemispheres.

Accepted Answer

Answer: True. Solution: The total surface area of such a solid is indeed the sum of the curved surface areas of the cylinder and the two hemispheres, as the flat surfaces are not exposed.

Question 45

The volume of a solid formed by combining two basic solids is the sum of the volumes of the individual solids.

Accepted Answer

Answer: True. Solution: When calculating the volume of a composite solid, the volume is the sum of the volumes of its individual components, as no volume is lost in the process of combining them.

Question 46

In a composite solid formed by a cylinder and a hemisphere, the total surface area includes the base area of the hemisphere.

Accepted Answer

Answer: False. Solution: The total surface area of a composite solid does not include the base area of the hemisphere when it is joined with another solid.

Question 47

When calculating the curved surface area of a toy made by combining a cone and a hemisphere, the base areas of the cone and hemisphere are included.

Accepted Answer

Answer: False. Solution: The base areas of the cone and hemisphere are not included when calculating the curved surface area, as they are not exposed surfaces.

Question 48

When calculating the surface area of a composite solid formed by joining two basic solids, the surface area of the internal surfaces that are not visible should be included.

Accepted Answer

Answer: False. Solution: The surface area of internal surfaces that are not visible is not included in the total surface area calculation of a composite solid.

Question 49

When calculating the surface area of a composite solid, the base area of a hemisphere attached to a cube is included in the total surface area.

Accepted Answer

Answer: False. Solution: The base area of the hemisphere is not included in the total surface area because it is attached to the cube, and thus not exposed.

Question 50

The total surface area of a composite solid is always the sum of the surface areas of the individual solids.

Accepted Answer

Answer: False. Solution: The total surface area of a composite solid is not simply the sum of the surface areas of the individual solids, as some areas may be internal and not exposed.

Question 51

The total surface area of a solid formed by a cylinder with two hemispheres on its ends is calculated by summing the curved surface areas of the cylinder and the two hemispheres.

Accepted Answer

Answer: True. Solution: The total surface area of such a solid is indeed the sum of the curved surface areas of the cylinder and the two hemispheres, as the flat surfaces are not exposed.

Question 52

In a composite solid where a hemisphere is mounted on a cube, the surface area of the face of the cube where the hemisphere is attached is included in the total surface area.

Accepted Answer

Answer: False. Solution: The surface area of the face of the cube where the hemisphere is attached is not included in the total surface area, as it is covered by the hemisphere.

Question 53

When calculating the total surface area of a composite solid, the internal surfaces where two solids join are included in the calculation.

Accepted Answer

Answer: False. Solution: The internal surfaces where two solids join are not visible and hence not included in the total surface area calculation.

Question 54

For a composite solid consisting of a cone and a hemisphere, the base radius of the cone must be equal to the radius of the hemisphere for a smooth surface.

Accepted Answer

Answer: True. Solution: To ensure a smooth surface where the cone and hemisphere meet, their base radii must be equal.

Question 55

The volume of a composite solid is always the sum of the volumes of its individual components.

Accepted Answer

Answer: True. Solution: When calculating the volume of a composite solid, the total volume is the sum of the volumes of the individual components, as there is no overlap in volume.

Question 56

A cylinder with two hemispheres at its ends has a total surface area equal to the sum of the curved surface area of the cylinder and the curved surface areas of the hemispheres.

Accepted Answer

Answer: True. Solution: The total surface area of such a composite solid is calculated by adding the curved surface area of the cylinder and the curved surface areas of the two hemispheres, as the base areas of the hemispheres are not exposed.

Question 57

When calculating the surface area of a composite solid formed by a cone and a hemisphere, the base area of the hemisphere is included in the total surface area.

Accepted Answer

Answer: False. Solution: The base area of the hemisphere is not included in the total surface area calculation because it is covered by the cone, leaving only the curved surface areas exposed.

Question 58

The total surface area of a composite solid made of a cylinder with two hemispheres attached at both ends is calculated by adding the curved surface areas of the cylinder and the two hemispheres.

Accepted Answer

Answer: True. Solution: The total surface area of such a composite solid is indeed the sum of the curved surface areas of the cylinder and the two hemispheres, as only these surfaces are visible.

Surface Areas and Volumes

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Surface Area of Composite Solids

Volume of Composite Solids

Curved Surface Area Calculations

Boundary Conditions in Composite Solids

Mathematical Constraints in Volume Calculations

Examples

Exercises

Summary

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Surface Area of Composite Solids

Volume of Composite Solids

Curved Surface Area Calculations

Boundary Conditions in Composite Solids

Mathematical Constraints in Volume Calculations

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Multiple Choice Questions

Q1.A cylindrical tank with a hemispherical bottom has a total height of 5 m and a diameter of 4 m. Calculate the total surface area of the tank. (Take π=3.14\pi = 3.14π=3.14)

Correct Answer: B

Q2.A cylindrical tank has a hemispherical depression at one end. If the height of the cylinder is hhh and the radius of both the cylinder and hemisphere is rrr, what is the total surface area of this structure?

Correct Answer: A

Q3.What is the total surface area of a solid formed by a cylinder with two hemispheres attached at its ends?

Correct Answer: A

Q4.A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm14 \text{ cm}14 cm and the total height of the vessel is 13 cm13 \text{ cm}13 cm. Find the inner surface area of the vessel.

Correct Answer: B

Q5.A composite solid is formed by joining a hemisphere and a cone, both having the same base radius of 4 cm. If the height of the cone is 6 cm, find the total surface area of the solid. (Take π=3.14\pi = 3.14π=3.14)

Correct Answer: C

Q6.A decorative block is made of a cube with a hemisphere on top. If the edge of the cube is 5 cm and the diameter of the hemisphere is 4.2 cm, what is the total surface area of the block?

Correct Answer: B

Q7.A medicine capsule is in the shape of a cylinder with two hemispheres attached at its ends. If the length of the capsule is 14 mm and the diameter is 5 mm, what is the surface area of the capsule?

Correct Answer: A

Q8.A cylindrical tank has a height of 1.45 m and a radius of 30 cm. A hemispherical depression is made at one end. What is the total surface area of the tank?

Correct Answer: A

Q9.A decorative block is made of a cube with edge length 5 cm and a hemisphere with a diameter of 4.2 cm placed on top. Calculate the total surface area of the block, excluding the base of the hemisphere.

Correct Answer: A

Q10.What is the formula for the curved surface area (CSA) of a cylinder with radius rrr and height hhh?

Correct Answer: B

Correct Answer: A

Q12.A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. What is the volume of the toy?

Correct Answer: A

Q13.A medicine capsule is in the shape of a cylinder with two hemispheres attached at each end. If the total length of the capsule is 14 mm and the diameter is 5 mm, what is the total surface area of the capsule?

Correct Answer: A

Q14.A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8g mass.

Correct Answer: B

Q15.A medicine capsule is in the shape of a cylinder with two hemispherical ends. The length of the entire capsule is 14 mm and the diameter is 5 mm. Find its surface area. (Take π=227\pi = \frac{22}{7}π=722​)

Correct Answer: B

Q16.A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Correct Answer: B

Q17.A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Correct Answer: A

Correct Answer: B

Q19.A vessel is shaped like a cylinder with two hemispherical ends. The length of the vessel is 14 cm and the diameter is 5 cm. What is the total surface area of the vessel? (Use π=3.14\pi = 3.14π=3.14)

Correct Answer: A

Q20.A toy is made by combining a hemisphere and a cone. If the radius of the base of the cone and the hemisphere is rrr, and the slant height of the cone is lll, what is the total surface area of the toy?

Correct Answer: A

Q21.A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, surmounted by another cylinder of height 60 cm and radius 8 cm. Calculate the mass of the pole, given that 1 cm³ of iron has approximately 8g mass.

Correct Answer: B

Q22.A toy is made by placing a cone of height 6 cm on a hemisphere with a radius of 3 cm. If the slant height of the cone is 6.5 cm, what is the total surface area of the toy? (Use π=3.14\pi = 3.14π=3.14)

Correct Answer: C

Q23.A medicine capsule is in the shape of a cylinder with two hemispheres attached at each end. The total length of the capsule is 14 mm and the diameter is 5 mm. What is the surface area of the capsule? (Use π=3.14\pi = 3.14π=3.14)

Correct Answer: B

Q24.A tent is in the shape of a cylinder surmounted by a conical top. The height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m. Calculate the total area of the canvas used for making the tent.

Correct Answer: A

Q25.A toy is made by combining a hemisphere and a cone with equal radii. If the radius of both the hemisphere and the cone is 3 cm, and the height of the cone is 4 cm, what is the total surface area of the toy?

Correct Answer: C

Q26.A toy is made by mounting a cone on a hemisphere. If the radius of both the cone and hemisphere is 2 cm and the height of the cone is 2 cm, what is the total surface area of the toy? (Take π=3.14\pi = 3.14π=3.14)

Correct Answer: A

Q27.A wooden toy is in the form of a cone mounted on a hemisphere. The radius of the hemisphere and the base of the cone is 2 cm, and the height of the cone is 2 cm. Calculate the volume of the toy. (Take π=3.14\pi = 3.14π=3.14)

Correct Answer: D