Question

what is the volume of a sphere with a radius of 5.9 in, rounded to the nearest tenth of a cubic inch?

Explanation:

Step1: Recall sphere volume formula

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

Step2: Substitute radius $r=5.9$ in

$$ V = \frac{4}{3}\pi (5.9)^3 $$

First calculate $(5.9)^3$: $5.9 \times 5.9 = 34.81$, then $34.81 \times 5.9 = 205.379$.

Step3: Compute the volume

$$ V = \frac{4}{3} \times \pi \times 205.379 \approx \frac{4}{3} \times 3.1416 \times 205.379 $$

Calculate $\frac{4}{3} \times 3.1416 \approx 4.1888$, then $4.1888 \times 205.379 \approx 860.3$

Answer:

$860.3$ cubic inches