Question

what is the approximate volume of a tree trunk if the trunk is 13 feet tall with a circumference of 4.5 feet? recall that the circumference of a circle is equal to pi times its diameter. a. 17.16ft³ b. 20.95ft³ c. 33.09ft³ d. 27.14ft³

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 \(r\).
From \(C=2\pi r\), we get \(r=\frac{C}{2\pi}\). Substituting \(C = 4.5\) feet, \(r=\frac{4.5}{2\pi}\approx\frac{4.5}{2\times3.14}\approx0.7165\) feet.

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

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given \(h = 13\) feet and \(r\approx0.7165\) feet.
First, calculate \(r^{2}=(0.7165)^{2}\approx0.5134\). Then \(V=\pi\times0.5134\times13\approx3.14\times0.5134\times13\approx20.95\) \(ft^{3}\).

Answer:

B. \(20.95\ ft^{3}\)