Surface Areas and Volumes: Most Important 50 MCQ

Surface Areas and Volumes

What is the formula for the volume of a sphere with radius r?
a)
$\frac{4}{3} π r^{3}$
b)
$π r^{2}$
c)
$4 π r^{3}$
d)
$π r^{3}$
Answer: a)
$\frac{4}{3} π r^{3}$
What is the total surface area of a cube with edge $a$ ?
a) 6 a
b)
$6 a^{2}$
c)
$a^{3}$
d)
$2 a^{2}$
Answer: b)
$6 a^{2}$
Which of the following is the curved surface area of a cylinder with radius $r$ and height $h$ ?
a)
$π r^{2} h$
b)
$2 π r h$
c)
$2 π r^{2} h$
d)
$π r^{2}$
Answer: b)
$2 π r h$
What is the formula for the volume of a cone with radius $r$ and height $h$ ?
a)
$π r^{2} h$
b)
$\frac{1}{3} π r^{2} h$
c)
$\frac{4}{3} π r^{3}$
d)
$2 π r h$
Answer: b)
$\frac{1}{3} π r^{2} h$
The total surface area of a sphere is given by:
a)
$2 π r^{2}$
b)
$3 π r^{2}$
c)
$4 π r^{2}$
d)
$π r^{2}$
Answer: c)
$4 π r^{2}$
A solid cylinder has a height of 10 cm and base radius 3 cm. What is its volume? Use

$π = 3.14$

a)
$282.6 {cm}^{3}$
b)
$188.4 {cm}^{3}$
c)
$100 {cm}^{3}$
d)
$300 {cm}^{3}$
Answer: a)
$282.6 {cm}^{3}$
The radius of a sphere is doubled. By what factor does the volume increase?
a) 2
b) 4
c) 6
d) 8
Answer: d) 8
Find the curved surface area of a cone with radius 7 cm and slant height 10 cm. Use

$π = \frac{22}{7}$

a)
$220 {cm}^{2}$
b)
$154 {cm}^{2}$
c)
$140 {cm}^{2}$
d)
$200 {cm}^{2}$
Answer: a)
$220 {cm}^{2}$
The height of a cylinder is twice the radius of its base. What is the ratio of its volume to the total surface area?
a) 1:1
b) 2:1
c) 3:1
d) 4:1
Answer: b) 2:1
A cone and a cylinder have the same radius and height. What is the ratio of their volumes?
a) 1:1
b) 1:2
c) 1:3
d) 2:3
Answer: c) 1:3
A toy is in the form of a hemisphere surmounted by a cone. If the height of the cone is 6 cm and the diameter of the hemisphere is 4 cm, find the volume of the toy. Use

$π = 3.14$

a)
$100.48 {cm}^{3}$
b)
$102.67 {cm}^{3}$
c)
$120.48 \, \text{cm}^3$
d)
$130 \, \text{cm}^3$
Answer: b)
$102.67 {cm}^{3}$
A cylindrical vessel is filled with water and has a height of 10 cm and radius 7 cm. If a solid sphere with radius 3 cm is immersed, what will be the new height of the water level? Use

$π = \frac{22}{7}$

a) 10.45cm
b) 10.36cm
c) 10.50cm
d) 10.30cm
Answer: b) 10.36cm
A hollow cylindrical pipe has an external radius of 5 cm and an internal radius of 3 cm. If the height of the pipe is 10 cm, find the volume of the material used. Use

$π = 3.14$

a)
$376.8 {cm}^{3}$
b)
$400 {cm}^{3}$
c)
$452.16 {cm}^{3}$
d)
$500 {cm}^{3}$
Answer: a)
$376.8 {cm}^{3}$
A cube is inscribed in a sphere of radius $r$ . What is the ratio of the surface area of the cube to that of the sphere?
a) 1:2
b) 1:3
c) 6:4
d) 3:2
Answer: b) 1:3
The height and radius of a cone are both doubled. By what factor does its volume increase?
a) 2
b) 4
c) 6
d) 8
Answer: d) 8
A cylinder has a height of 20 cm and radius of 7 cm. A cone is carved out from it with the same radius and height. Find the volume of the remaining solid. Use

$π = \frac{22}{7}$

a)
$3080 {cm}^{3}$
b)
$3140 {cm}^{3}$
c)
$3300 {cm}^{3}$
d)
$3020 {cm}^{3}$
Answer: a)
$3080 {cm}^{3}$
A hemispherical bowl has a diameter of 14 cm. Find the cost of painting its inner surface at
$₹5$ per square cm. Use

$\pi = \frac{22}{7}$

a) ₹770
b) ₹1078
c) ₹800
d) ₹980
Answer: a) ₹770
A sphere is melted to form 8 smaller spheres of equal radii. What is the ratio of the radius of the original sphere to that of a smaller sphere?
a) 1:2
b) 1:3
c) 1:4
d) 1:8
Answer: b) 1:2
A cylinder is inscribed in a sphere of radius r. What is the ratio of the volume of the cylinder to that of the sphere?
a) 1:2
b) 1:3
c) 2:3
d) 1:4
Answer: c) 2:3
A hemisphere is surmounted on a cone of equal radius. If the height of the cone is equal to twice the radius, find the ratio of their volumes.
a) 1:2
b) 1:3
c) 2:3
d) 1:4
Answer: c) 2:3
What is the volume of a cube with edge length $a = 5 cm$ ?
a)
$25 {cm}^{3}$
b)
$50 {cm}^{3}$
c)
$100 {cm}^{3}$
d)
$125 {cm}^{3}$
Answer: d)
$125 {cm}^{3}$
The formula for the curved surface area of a cylinder is:
a)
$2 π r h$
b)
$π r^{2} h$
c)
$π r^{2}$
d)
$2 π r^{2} h$
Answer: a)
$2 π r h$
If the diameter of a sphere is 14 cm, what is its radius?
a) 7 cm
b) 14 cm
c) 21 cm
d) 28 cm
Answer: a) 7 cm
The total surface area of a hemisphere is given by:
a)
$2 π r^{2}$
b)
$3 π r^{2}$
c)
$4 π r^{2}$
d)
$π r^{2}$
Answer: b)
$3 π r^{2}$
Which shape has the largest volume for a given surface area?
a) Cube
b) Sphere
c) Cylinder
d) Cone
Answer: b) Sphere
A cylinder has a height of 14 cm and radius 7 cm. What is its total surface area? Use

$π = \frac{22}{7}$

a)
$462 {cm}^{2}$
b)
$616 {cm}^{2}$
c)
$968 {cm}^{2}$
d)
$1436 \, \text{cm}^2$
Answer: c)
$968 {cm}^{2}$
A hollow hemisphere has an external radius of 7 cm and an internal radius of 5 cm. Find the volume of the material used. Use

$π = \frac{22}{7}$
a)
$154 {cm}^{3}$
b)
$462 {cm}^{3}$
c)
$616 {cm}^{3}$
d)
$770 {cm}^{3}$
Answer: c)
$616 {cm}^{3}$
A cone has a base radius of 4 cm and height 3 cm. Find its slant height.
a) 4 cm
b) 5 cm
c) 6 cm
d) 7 cm
Answer: b) 5 cm
A cone has a height of 12 cm and a base radius of 5 cm. What is its total surface area? Use

$π = 3.14$
a)
$226.2 {cm}^{2}$
b)
$188.4 {cm}^{2}$
c)
$157 {cm}^{2}$
d)
$314 {cm}^{2}$
Answer: a)
$226.2 {cm}^{2}$
A solid sphere is melted and recast into 64 smaller spheres of equal size. If the radius of the smaller sphere is 2 cm, find the radius of the original sphere.
a) 8 cm
b) 10 cm
c) 12 cm
d) 16 cm
Answer: a) 8 cm
A cylindrical tank has a radius of 5 m and height 14 m. Find its capacity in liters. Use

$\pi = \frac{22}{7}$

and

$1 m^{3} = 1000 liters$
a) 2200 liters
b) 11000 liters
c) 55000 liters
d) 22000 liters
Answer: d) 22000 liters
A hemispherical bowl of radius 7 cm is filled with water. If water is poured into cylindrical bottles with radius 3 cm and height 14 cm, how many bottles can be filled? Use

$π = \frac{22}{7}$
a) 5
b) 6
c) 7
d) 8
Answer: b) 6
A cuboidal water tank measures 6 m × 4 m × 2.5 m. Find the total cost of painting its outer surface at $₹10$ per

$\text{m}^2$

.
a) ₹400
b) ₹500
c) ₹600
d) ₹700
Answer: c) ₹600
A cone is inscribed in a hemisphere of radius $r$ . The height of the cone equals the radius of the hemisphere. Find the ratio of their volumes.
a)
$1 : 2$
b)
$2 : 3$
c)
$1 : 3$
d)
$3 : 4$
Answer: b)
$2 : 3$
A solid toy is made of a hemisphere mounted on a cylinder. If the radius of both is 3 cm and the height of the cylinder is 6 cm, find the total surface area. Use

$\pi = \frac{22}{7}$

a)
$198 {cm}^{2}$
b)
$216 {cm}^{2}$
c)
$254 {cm}^{2}$
d)
$286 {cm}^{2}$
Answer: d)
$286 {cm}^{2}$
A solid iron pole consists of a cylinder of height 7 m and radius 4 m, surmounted by a cone of height 3 m and radius 4 m. Find the total volume of the pole. Use

$\pi = \frac{22}{7}$

a)
$440 \, \text{m}^3$
b)
$528 \, \text{m}^3$
c)
$560 \, \text{m}^3$
d)
$616 \, \text{m}^3$
Answer: b)
$528 \, \text{m}^3$
A tent is in the shape of a cylinder surmounted by a cone. The height of the cylindrical part is 3 m, the diameter of the base is 6 m, and the slant height of the conical part is 5 m. Find the area of the canvas used. Use

$\pi = 3.14$

a)
$113.04 \, \text{m}^2$
b)
$150.72 \, \text{m}^2$
c)
$176.58 \, \text{m}^2$
d)
$188.4 \, \text{m}^2$
Answer: c)
$176.58 \, \text{m}^2$
A sphere is melted and cast into a hollow cylinder with external radius 5 cm, internal radius 4 cm, and height 7 cm. Find the radius of the sphere. Use

$\pi = \frac{22}{7}$

a) 4 cm
b) 5 cm
c) 6 cm
d) 7 cm
Answer: b) 5 cm
A solid is made up of a hemisphere, a cylinder, and a cone of equal radius 7 cm. The height of the cone and cylinder is 10 cm each. Find the total volume of the solid. Use

$\pi = \frac{22}{7}$

a)
$2464 \, \text{cm}^3$
b)
$3080 \, \text{cm}^3$
c)
$4620 \, \text{cm}^3$
d)
$6160 \, \text{cm}^3$
Answer: a)
$2464 \, \text{cm}^3$
A medicine capsule is in the shape of a cylinder with hemispherical ends. If the length of the capsule is 14 mm and its diameter is 5 mm, find its total surface area. Use

$\pi = \frac{22}{7}$

a)
$220 \, \text{mm}^2$
b)
$231 \, \text{mm}^2$
c)
$308 \, \text{mm}^2$
d)
$385 \, \text{mm}^2$
Answer: b)
$231 \, \text{mm}^2$
A hemispherical dome has a radius of 14 m. Find its total surface area. Use
$\pi = \frac{22}{7}$

a)
$1846 \, \text{m}^2$
b)
$1232 \, \text{m}^2$
c)
$1540 \, \text{m}^2$
d)
$1760 \, \text{m}^2$
Answer: b)
$1232 \, \text{m}^2$
A solid metal sphere of radius 7 cm is melted and recast into 8 smaller spheres of equal size. Find the radius of each smaller sphere.
a) 3.5 cm
b) 4 cm
c) 3 cm
d) 2.5 cm
Answer: a) 3.5 cm
A cone has a slant height of 10 cm and a base diameter of 12 cm. Find its curved surface area. Use

$\pi = 3.14$

a)
$360 \, \text{cm}^2$
b)
$376.8 \, \text{cm}^2$
c)
$420 \, \text{cm}^2$
d)
$314 \, \text{cm}^2$
Answer: a)
$360 {cm}^{2}$
A cube has a total surface area of 96

$\text{cm}^2$

Find its volume.
a)
$64 {cm}^{3}$
b)
$72 {cm}^{3}$
c)
$48 {cm}^{3}$
d)
$27 {cm}^{3}$
Answer: a)
$64 {cm}^{3}$
The slant height of a cone is 13 cm, and its height is 12 cm. Find the radius of the cone.
a) 3 cm
b) 4 cm
c) 5 cm
d) 6 cm
Answer: c) 5 cm
A spherical balloon is being inflated. If the radius increases from 7 cm to 14 cm, by what factor does the surface area increase?
a) 2
b) 4
c) 6
d) 8
Answer: b) 4
A cylinder has a height of 10 cm and radius 7 cm. If the top and bottom are open, find the surface area. Use

$π = \frac{22}{7}$
a)
$440 \, \text{cm}^2$
b)
$528 \, \text{cm}^2$
c)
$308 \, \text{cm}^2$
d)
$704 \, \text{cm}^2$
Answer: b)
$528 \, \text{cm}^2$
A cuboid has dimensions 8 cm × 6 cm × 4 cm. Find the length of its diagonal.
a) 8 cm
b) 9 cm
c) 10 cm
d) 12 cm
Answer: c) 10 cm
A hollow cone has a base radius of 7 cm, height of 24 cm, and slant height of 25 cm. Find the total surface area. Use

$\pi = \frac{22}{7}$

a)
$330 \, \text{cm}^2$
b)
$550 \, \text{cm}^2$
c)
$770 \, \text{cm}^2$
d)
$924 \, \text{cm}^2$
Answer: c)
$770 \, \text{cm}^2$
A hemisphere has a curved surface area of

$1386 \, \text{cm}^2$

Find its radius. Use

$\pi = \frac{22}{7}$

a) 14 cm
b) 21 cm
c) 28 cm
d) 7 cm
Answer: b) 21 cm

Surface Areas and Volumes

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