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

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What is the formula for the volume of a sphere?

V = (4/3)πr^3

Explanation

Volume of a sphere is proportional to the cube of its radius.

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

A = 4πr^2

Explanation

Surface area of a sphere is proportional to the square of its radius.

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

6 cm

Explanation

Radius is half of the diameter.

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

The diameter is twice the radius

Explanation

Diameter is double the radius.

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

9 units

Explanation

Volume formula rearrangement to find radius.

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

250π cm^3

Explanation

Half the volume of a sphere with same radius.

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

2:1

Explanation

Sphere's volume is two-thirds of circumscribed cylinder.

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

9 units

Explanation

Surface area formula rearrangement to find radius.

What is the formula for the volume of a hemisphere?

V = (2/3)πr^3

Explanation

Volume of a hemisphere is two-thirds of sphere.

#10

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

0.79

Explanation

Radius decreases by cube root of volume change.

#11

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

600π cm^3

Explanation

Volume of inscribed sphere is half the cube's volume.

#12

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?

3 cm

Explanation

Cube's volume is 6 times sphere's volume.

#13

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?

4:1

Explanation

Cube's surface area is 4 times sphere's surface area.

#14

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

2:1

Explanation

Sphere's surface area is twice that of its circumscribed cylinder.

#15

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

√2r

Explanation

Cone's radius is square root of twice the sphere's radius.

#16

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

2:1

Explanation

Sphere's volume is twice that of its inscribed cone.

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

What is the formula for the volume of a sphere?

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

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

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

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

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

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

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

What is the formula for the volume of a hemisphere?

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

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

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?

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?

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

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

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

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