Question

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

What is the volume of the cylinder?

Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.

Answer:______ft³

Answer 1

The formula of a volume of a cylinder:

`V=\pi r^2H`

We have

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

Therefore
`r=(1)/(2)\cdot(445)/(5)\ ft=(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`