Question

A right circular cylinder has a height of 22 1/4 ft and a diameter 2 2/5 times its height.

Answer 1

The formula of a volume of a cylinder:

$V=\pi r^2H$

We have

$H=22\dfrac{1}{4}\ ft=\dfrac{22\cdot4+1}{4}\ ft=\dfrac{89}{4}\ ft=22.25\ ft\\\\2r=2\dfrac{2}{5}\cdot\22dfrac{1}{4}=\dfrac{2\cdot5+2}{5}\cdot\dfrac{89}{4}=\dfrac{12}{5}\cdot\dfrac{89}{4}=\dfrac{3}{5}\cdot\dfrac{89}{1}=\dfrac{445}{5}\ ft$

Therefore $r=\dfrac{1}{2}\cdot\dfrac{445}{5}\ ft=\dfrac{445}{10}\ ft=44.5\ ft$

Substitute:

$V=\pi\cdot\left(44.5)^2(22.25)=44060.562\pi\ ft^3\approx44060.562\cdot3.14\approx138350.16\ ft^3$