Question

An ash borer is an invasive pest whose larvae eat the pulp of ash trees as they mature. A park ranger has a tree that is infested with ash borers. She estimates they have eaten approximately 40% of the tree's pulp. If the ash tree's trunk has a radius of 2 feet and a height of 15 feet, what was the total volume of the tree trunk before the ash borers started eating it?

Answer 1

`188.6` cubic feet

Explanation:

Let r, h denotes radius and height of the tree's trunk.

Radius of the tree's trunk = 2 feets

Height of the tree's trunk = 15 feets

The tree's trunk is in the shape of a cylinder.

Volume of cylinder (tree's trunk)
`=\pi r^2h`

Put
`r=2\,,\,h=15`

Volume of the tree's trunk
`=\pi (2)^2(15)=60\pi` cubic feet

Put
`\pi=(22)/(7)`

So,

Volume of the tree's trunk
`=60((22)/(7))=(1320)/(7)=188.6` cubic feet