Question

what is the volume of a sphere with a radius of 31.6 cm, rounded to the nearest tenth of a cubic centimeter?

Explanation:

Step1: Recall sphere volume formula

The volume $V$ of a sphere is given by $V = \frac{4}{3}\pi r^3$, where $r$ is the radius.

Step2: Substitute radius value

Substitute $r = 31.6$ cm into the formula:
$V = \frac{4}{3}\pi (31.6)^3$
First calculate $(31.6)^3$:
$31.6^3 = 31.6 \times 31.6 \times 31.6 = 31554.496$

Step3: Compute intermediate volume

Multiply by $\frac{4}{3}$:
$\frac{4}{3} \times 31554.496 \approx 42072.6613$
Then multiply by $\pi$ (use $\pi \approx 3.14159$):
$V \approx 42072.6613 \times 3.14159 \approx 132175.6$

Answer:

$132175.6$ cubic centimeters