Question

score: 2/5 penalty: 1 off
question
what is the volume of a hemisphere with a diameter of 30.3 ft, rounded to the nearest tenth of a cubic foot?
answer attempt 1 out of 2
$\text{ft}^3$
submit answer

Explanation:

Step1: Find radius from diameter

The radius $r$ is half the diameter.
$r = \frac{30.3}{2} = 15.15$ ft

Step2: Use hemisphere volume formula

The volume $V$ of a hemisphere is $\frac{2}{3}\pi r^3$.
$V = \frac{2}{3} \times \pi \times (15.15)^3$

Step3: Calculate the cube of radius

$(15.15)^3 = 15.15 \times 15.15 \times 15.15 = 3483.325875$

Step4: Compute intermediate volume value

$V = \frac{2}{3} \times \pi \times 3483.325875 \approx \frac{2}{3} \times 10943.19$
$V \approx 7295.46$

Step5: Round to nearest tenth

Round 7295.46 to one decimal place.
$V \approx 7295.5$

Answer:

$7295.5$ ft³