Question

what is the volume of a hemisphere with a radius of 39.4 ft, rounded to the nearest tenth of a cubic foot?

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 $r=39.4$ ft

$V = \frac{2}{3} \pi (39.4)^3$
First calculate $(39.4)^3$:
$39.4^3 = 39.4 \times 39.4 \times 39.4 = 1552.36 \times 39.4 = 61162.984$

Step3: Compute the volume

$V = \frac{2}{3} \times \pi \times 61162.984$
$V = \frac{122325.968}{3} \times \pi \approx 40775.3227 \times 3.1416 \approx 128109.7$

Answer:

$128109.7$ cubic feet