Question

Consider this sphere with a diameter of 5 m.

What can be concluded about the sphere? Check all
that apply,
The sphere has a radius of 10 cm.
The diameter measure is substituted into the
formula to find the volume.
5 m
The radius is half the diameter.
The formula to apply is y=- Bh
The volume of the sphere is two-thirds the volume
of a cylinder with the same radius and height.

Answer 1

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Answer:

• The radius is half the diameter.
• The volume of the sphere is two-thirds the volume of a cylinder with the same radius and height.

Explanation:

Regardless of the diameter, the radius is half the diameter. For this sphere, it is 5/2 m = 2.5 m.

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The height of the sphere is equal to its diameter, so is 2r. The volume of a cylinder with radius r and height 2r is ...

V = πr²h = πr²(2r) = 2πr³

The volume of a sphere with radius r is ...

V = 4/3πr³

Then the ratio of sphere volume to cylinder volume is ...

(4/3πr³)/(2πr³) = (4/3)/2 = 2/3

The sphere volume is 2/3 that of a cylinder with the same radius and height.