Question

question 27 of 39
what is the approximate volume of a tree trunk if the trunk is 15 feet tall with
a circumference of 4.5 feet?
recall that the circumference of a circle is equal to pi times its diameter.

a. 33.92 ft³
b. 23.33 ft³
c. 24.17 ft³
d. 43.12 ft³

Explanation:

Step1: Find the radius from the circumference

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=4.5\) feet, we can solve for \(r\).

$$r=\frac{C}{2\pi}=\frac{4.5}{2\pi}$$

Step2: Calculate the volume of the cylinder (tree - trunk)

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Substitute \(h = 15\) feet and \(r=\frac{4.5}{2\pi}\) into the formula.

$$V=\pi(\frac{4.5}{2\pi})^{2}\times15$$

$$V=\pi\times\frac{20.25}{4\pi^{2}}\times15$$

$$V=\frac{20.25\times15}{4\pi}$$

$$V=\frac{303.75}{4\pi}$$

Using \(\pi\approx3.14\), we have \(V=\frac{303.75}{4\times3.14}=\frac{303.75}{12.56}\approx33.92\mathrm{ft}^3\)

Answer:

A. \(33.92\mathrm{ft}^3\)