find the volume of this cone. round to the nearest tenth.

Explanation:

Step1: Recall volume formula

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

Step2: Identify values

Here, $r = 4$ in and $h=7$ in.

Step3: Substitute values

$V=\frac{1}{3}\pi\times(4)^{2}\times7=\frac{1}{3}\pi\times16\times7=\frac{112\pi}{3}$ in³.

Step4: Calculate and round

$V=\frac{112\pi}{3}\approx\frac{112\times 3.14159}{3}\approx117.3$ in³.

Answer:

$117.3$ in³