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

1. Break Down the Problem

To find the volume of a sphere, we need to use the formula for the volume of a sphere, which is: $V = \frac{4}{3} \pi r^3$ where $V$ is the volume and $r$ is the radius.

2. Relevant Concepts

In this case, the radius $r$ is given as 5 inches.

3. Analysis and Detail

Substituting the radius into the formula: $V = \frac{4}{3} \pi (5)^3$

Calculating $(5)^3$: $(5)^3 = 125$

Substituting back into the volume formula: $V = \frac{4}{3} \pi (125)$ $V = \frac{500}{3} \pi$

Now, approximating $\pi$ as 3.14: $V \approx \frac{500}{3} \times 3.14$

Calculating $\frac{500 \times 3.14}{3}$: $V \approx \frac{1570}{3} \approx 523.3333$

4. Verify and Summarize

When rounded to the nearest tenth: $V \approx 523.3 \text{ cubic inches}$

Final Answer

The volume of the sphere is approximately 523.3 cubic inches.