Question

Question 18 of 44What is the approximate volume of a tree trunk if the trunk is 15 feet tall witha circumference of 4.5 feet?A. 43.12 ft3B. 24.43 ft?C. 33.92 ft3O D. 23.33 ft

Answer 1

A trunk is a cylinder which means that its volume is given by the product between the area of its circular base and its height. We have the height but we need to find the area of the base. We do know the circumference. The circumference of a circle of radius r is given by:

`2\pi r`

So with the circunference we can find the radius of the base and with the radius we can find its area since the area of a circle is given by:

`\pi r^2`

So knowing that the circumference is 4.5 ft the equation for the radius is:

`2\pi r=4.5`

We divide both sides by 2π:

`\begin{gathered} (2\pi r)/(2\pi)=(4.5)/(2\pi) \\ r=(4.5)/(2\pi) \end{gathered}`

With the radius we find the area of the base:

`A=\pi\cdot((4.5)/(2\pi))^2=(\pi)/(\pi^2)\cdot5.0625=(5.0625)/(\pi)`

Then we multiply this by the height:

`15\cdot(5.0625)/(\pi)=24.17`

The closest option to this value is 24.43 ft³ so the answer is option B.