Question

a sphere has a radius of 5 inches. what is its volume? sphere $v = \frac{4}{3}\pi r^{3}$ 1. substitute the radius into the formula: $v = \frac{4}{3}\pi(5^{3})$ 2. evaluate the power: $v = \frac{4}{3}\pi(125)$ 3. simplify: $v = \square\pi$ in$^{3}$

Explanation:

Step1: Substitute the radius

Given the formula for the volume of a sphere \(V=\frac{4}{3}\pi r^{3}\), and \(r = 5\) inches. Substitute \(r\) into the formula: \(V=\frac{4}{3}\pi(5^{3})\)

Step2: Evaluate the power

Calculate \(5^{3}=5\times5\times5 = 125\). So the formula becomes \(V=\frac{4}{3}\pi(125)\)

Step3: Simplify

Multiply \(\frac{4}{3}\times125=\frac{4\times125}{3}=\frac{500}{3}\)

Answer:

\(\frac{500}{3}\)