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)
$\frac{9648}{18}$ = $\pi$r²
536 = $\pi$r²
$\frac{536}{ \pi}$ = r²
$\sqrt{ \frac{536}{ \pi } }$ = 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

$\frac{13.06}{2} = r$
r ≈ 6.53  ( the radius of the small radius )

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