Question

The volume of a tree stump can be modeled by considering it as a right cylinder. Charlotte measures its circumference as 209 in and its volume as 33370 cubic inches. Find the height of the stump in feet. Round your answer to the nearest tenth if necessary.

Answer 1

Given:

A tree stump considering a right cylinder.

The circumference of the right cylinder, C=209 inches.

The volume of the right cylinder, V=33370 cubic inches.

Required:

We need to find the height of the stump in feet.

Explanation:

The base of the right cylinder is a circle.

Consider the formula to find the circumference of the circle.

$C=2\pi r$

Substitute C = 209 in the formula.

$209=2\pi r$$Divide\text{ both sides by }2\pi.$

$\frac{209}{2\pi}=\frac{2\pi r}{2\pi}$

$\frac{209}{2\pi}=r$

$We\text{ get the radius of the tree stump, r=}\frac{209}{2\pi}.$

Consider the formula to find the volume of the right cylinder.

$V=\pi r^2h$

$Substitute\text{ V=33370 and r =}\frac{209}{2\pi}in\text{ the formula.}$

$33370=\pi(\frac{209}{2\pi})^2h$

$33370=\pi\times\frac{209^2}{2^2\pi^2}\times h$

$33370=\frac{209^2}{4\pi^}\times h$

Solve for h.

$33370\times\frac{4\pi}{209^2}=h$

$33370\times\frac{4\times3.14}{43681}=h$

$9.5952=h$

$h=9.5952in$

We know that 1 foot = 12 inches.

Divide the height by 12 to get convert from inches to feet.

$h=\frac{9.5952}{12}feet$

$h=0.8feet$

Final answer:

The height of the stump is 0.8 feet.