Question

question
what is the volume of a hemisphere with a diameter of 56.7 in, rounded to the nearest tenth of a cubic inch?

Explanation:

Step1: Find radius from diameter

The radius $r$ is half the diameter.
$r = \frac{56.7}{2} = 28.35$ in

Step2: Recall hemisphere volume formula

Volume $V$ of a hemisphere is $\frac{2}{3}\pi r^3$.

Step3: Substitute radius into formula

$V = \frac{2}{3} \times \pi \times (28.35)^3$
First calculate $(28.35)^3 = 28.35 \times 28.35 \times 28.35 = 22722.624375$
Then $V = \frac{2}{3} \times \pi \times 22722.624375 \approx \frac{2}{3} \times 71393.09 \approx 47595.39$

Step4: Round to nearest tenth

Round $47595.39$ to one decimal place.

Answer:

$47595.4$ cubic inches