What is the volume of a sphere with a radius of 5 in, rounded to the nearest tenth of a cubic inch?

To find the volume of a sphere with a radius of 5 inches, we use the formula for the volume of a sphere:

$V = \frac{4}{3} \pi r^3$

where $V$ is the volume and $r$ is the radius.

1. Substitute the radius $r = 5$ inches into the formula:

$V = \frac{4}{3} \pi (5)^3$

2. Calculate $(5)^3$:

$(5)^3 = 5 \times 5 \times 5 = 125$

3. Substitute $125$ into the formula:

$V = \frac{4}{3} \pi \times 125$

4. Multiply $\frac{4}{3}$ by $125$:

$\frac{4}{3} \times 125 = \frac{500}{3}$

5. Now, multiply by $\pi$:

$V = \frac{500}{3} \pi$

6. Use the approximate value of $\pi \approx 3.14159$:

$V \approx \frac{500}{3} \times 3.14159$

7. Calculate $\frac{500}{3}$:

$\frac{500}{3} \approx 166.6667$

8. Multiply by $3.14159$:

$V \approx 166.6667 \times 3.14159 \approx 523.5988$

9. Round to the nearest tenth:

$V \approx 523.6$

Therefore, the volume of the sphere is approximately 523.6 cubic inches.