Question

question 44 of 44
what is the approximate volume of a tree trunk if the trunk is 12 feet tall with a circumference of 4.5 feet?
recall that the circumference of a circle is equal to pi times its diameter.
a. 21.17 ft³
b. 29.40 ft³
c. 25.92 ft³
d. 19.34 ft³

Explanation:

Step1: Find the radius from the circumference

Given $C = \pi d$, and $C = 4.5$ feet. So $d=\frac{C}{\pi}=\frac{4.5}{\pi}$ feet, and $r=\frac{d}{2}=\frac{4.5}{2\pi}$ feet.

Step2: Calculate the volume of the cylinder - shaped trunk

The volume formula for a cylinder is $V=\pi r^{2}h$. Substitute $r = \frac{4.5}{2\pi}$ and $h = 12$ into the formula.
\[

$$\begin{align*} V&=\pi\times(\frac{4.5}{2\pi})^{2}\times12\\ &=\pi\times\frac{4.5^{2}}{4\pi^{2}}\times12\\ &=\frac{4.5^{2}\times12}{4\pi}\\ &=\frac{20.25\times12}{4\pi}\\ &=\frac{243}{4\pi}\\ &\approx\frac{243}{4\times3.14}\\ &=\frac{243}{12.56}\\ &\approx19.34\text{ ft}^3 \end{align*}$$

\]

Answer:

D. $19.34$ ft$^3$