Volume and Surface Area of Spheres in Three-Dimensional Geometry Quiz

Test your knowledge on volume, surface area, and geometry of spheres with these questions. Learn key formulas and concepts.

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What is the formula for the volume of a sphere?

V = (4/3)πr

V = (4/3)πr^3

V = 4πr^3

V = πr^2

What is the formula for the surface area of a sphere?

A = 4πr^2

A = 2πr

A = πr^2

A = (4/3)πr^3

If the diameter of a sphere is 12 cm, what is its radius?

3 cm

6 cm

12 cm

24 cm

1 answered

What is the relationship between the diameter and the radius of a sphere?

The diameter is half the radius

The diameter is twice the radius

The diameter is three times the radius

There is no relationship between them

A sphere has a volume of 36π cubic units. What is its radius?

3 units

6 units

9 units

12 units

A hemisphere has a radius of 5 cm. What is its volume?

125π cm^3

250π cm^3

500π cm^3

625π cm^3

What is the ratio of the volume of a sphere to the volume of its circumscribed cylinder?

1:2

1:3

2:1

3:1

If the surface area of a sphere is 144π square units, what is its radius?

6 units

8 units

9 units

12 units

What is the formula for the volume of a hemisphere?

V = (2/3)πr^3

V = (4/3)πr^3

V = (1/2)πr^3

V = (2/3)πr

#10

If the volume of a sphere is halved, by what factor does its radius change?

0.5

0.63

0.79

0.87

#11

What is the formula for the lateral surface area of a hemisphere?

A = 2πr

A = πr^2

A = 3πr^2

A = 4πr^2

#12

If the diameter of a sphere is doubled, what happens to its volume?

It doubles

It quadruples

It becomes eight times

It becomes sixteen times

#13

What is the formula for the volume of a spherical segment?

V = (1/3)πh(3R^2 + r^2)

V = (1/6)πh(3R^2 + r^2)

V = (1/2)πh(R^2 + r^2)

V = (2/3)πh(R^2 + r^2)

#14

If the radius of a sphere is tripled, what happens to its surface area?

It triples

It quadruples

It becomes nine times

It becomes eighteen times

#15

What is the maximum volume of a sphere that can be inscribed in a cube with a side length of 10 cm?

500π cm^3

600π cm^3

800π cm^3

1000π cm^3

#16

A sphere and a cube have equal volumes. If the cube has a side length of 6 cm, what is the radius of the sphere?

2 cm

3 cm

4 cm

6 cm

#17

If a sphere is melted and recast into a cube, what is the ratio of the surface area of the cube to the surface area of the sphere?

1:4

2:3

3:2

4:1

#18

What is the ratio of the surface area of a sphere to the surface area of its circumscribed cylinder?

2:1

3:1

1:2

1:3

#19

A sphere and a cone have equal volumes. If the radius of the sphere is 'r', what is the radius of the cone?

r/2

√2r

#20

What is the ratio of the volume of a sphere to the volume of its inscribed cone?

1:2

2:1

1:3

3:1

#21

A sphere and a cylinder have the same height and radius. What is the ratio of their volumes?

2:1

3:2

1:1

4:3

#22

What is the maximum surface area of a cone that can be carved out of a sphere with radius 'r'?

πr^2

2πr^2

3πr^2

4πr^2

#23

What is the formula for the volume of the largest cone that can be cut out from a sphere?

V = (1/6)πR^3

V = (1/3)πR^3

V = (1/2)πR^3

V = (2/3)πR^3

#24

If a sphere is inscribed in a cube, what is the ratio of the volume of the sphere to the volume of the cube?

1:2

1:3

π:6

π:3

#25

What is the surface area of the largest sphere that can be carved out of a cube with edge length 'a'?

6a^2

8a^2

12a^2

16a^2