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The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches. What is the volume of the smaller cylinder?

The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches-example-1

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Hey there :)

The volume formula of a cylinder is:
V =
\pir²h

The volume of the larger volume is given to be 9648³ and the height is 18 in
We need to find the radius first

9648 =
\pir²(18)

(9648)/(18) =
\pi
536 =
\pi

(536)/( \pi) = r²

\sqrt{ (536)/( \pi ) } = r
r ≈ 13.06

The ratio of the big cylinder to small cylinder is:
18 : 9 (given height)
So the big cylinder is 2 times bigger than the small cylinder
Therefore the radius of the big cylinder is as well 2 times bigger


(13.06)/(2) = r
r ≈ 6.53 ( the radius of the small radius )

V (of small cylinder) =
\pi(6.53)²(9)
= 1206 in³
User Adalcar
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