Question

Which of the following polyhedra have the same volume?

Select each geometry shape which have the same volume.
A.
A hemisphere with a radius of 2 cm.
B.
A sphere with a radius of 14 cm.
C.
A cone with a radius of 2 cm and a height of 4 cm.
D.
A cylinder with a radius of 13 cm and a height of 13 cm.

Answer 1

A and C

Explanation:

We can eliminate poor choices by estimating their relative sizes. And we can check the remaining choices by finding the exact volumes.

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A hemisphere with radius 2, or a cone with dimensions of 4 or less, will have a much smaller volume than a sphere with radius 14. A cylinder with dimesions smaller than those of the sphere will have a smaller volume.

So, the only figures that might have similar volumes are the hemisphere and the cone.

Hemisphere

V = 1/2(4/3)πr³ = 2/3π(2 cm)³ = 16/3π cm³

Cone

V = 1/3πr²h = 1/3π(2 cm)²(4 cm) = 16/3πcm³

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The hemisphere (A) and the cone (C) have the same volume.