Question

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

Answer 1

Hey there :)

The volume formula of a cylinder is:
V =
`\pi`r²h

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 =
`\pi`r²(18)

`(9648)/(18)` =
`\pi`r²
536 =
`\pi`r²

`(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