Question

find the volume of the cone shown below. a. $392pi$ units$^3$ b. $392$ units$^3$ c. $1176pi$ units$^3$ d. $1176$ units$^3$

Explanation:

Step1: Recall cone volume formula

The volume $V$ of a cone is given by $V = \frac{1}{3}\pi r^2 h$, where $r$ is the radius of the base, and $h$ is the height of the cone.

Step2: Identify given values

From the diagram, $r = 7$ units, $h = 24$ units.

Step3: Substitute values into formula

$$\begin{align*} V &= \frac{1}{3}\pi (7)^2 (24)\\ &= \frac{1}{3}\pi \times 49 \times 24 \end{align*}$$

Step4: Calculate the numerical product

First compute $\frac{1}{3} \times 24 = 8$, then $8 \times 49 = 392$.
So $V = 392\pi$

Answer:

A. $392\pi$ units$^3$