Question

what is the volume of a hemisphere with a radius of 34.1 in, rounded to the nearest tenth of a cubic inch?

Explanation:

Step1: Recall hemisphere volume formula

The volume $V$ of a hemisphere is $\frac{2}{3}\pi r^3$, where $r$ is the radius.

Step2: Substitute radius $r=34.1$ in

$$V = \frac{2}{3} \pi (34.1)^3$$
First calculate $(34.1)^3$:
$34.1 \times 34.1 = 1162.81$, then $1162.81 \times 34.1 = 39651.821$

Step3: Compute the volume

$$V = \frac{2}{3} \times \pi \times 39651.821$$
$$V = \frac{79303.642}{3} \times \pi \approx 26434.547 \times 3.1416 \approx 83056.7$$

Answer:

$83056.7$ cubic inches