Question

A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 8 feet. Find the radius.

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Answer 1

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Answer:

6 feet

Explanation:

The volume of a cylinder is given by ...

V = πr^2·h

For a sphere, the volume is ...

V = 4/3πr^3

You want the volumes to be the same when h=8, so we have ...

πr^2·8 = 4/3πr^3

Dividing by πr^2, we have ...

8 = 4/3r

r = 3/4·8 = 6

The radius is 6 feet.