Question

the volume of a cone with radius r and height h is given by the formula $v = \frac{1}{3}\pi r^2 h$. a cone - shaped pile of sawdust has a base diameter of 28 feet, and is 12 feet tall. find the volume of the sawdust pile. $\square$ $\text{ft.}^3$ round your answer to the nearest hundredth if necessary. use 3.14 or the $\pi$ button on your calculator.

Explanation:

Step1: Calculate radius from diameter

The diameter is 28 ft, so radius $r = \frac{28}{2} = 14$ ft.

Step2: Substitute values into volume formula

Use $V=\frac{1}{3}\pi r^2 h$, with $r=14$, $h=12$, $\pi=3.14$.
$$V=\frac{1}{3} \times 3.14 \times 14^2 \times 12$$

Step3: Simplify the expression

First calculate $14^2=196$, then $\frac{1}{3} \times 12=4$.
$$V=3.14 \times 196 \times 4$$
$$V=3.14 \times 784$$
$$V=2461.76$$

Answer:

2461.76 ft.$^3$