Question

a baseball has a volume of 113.04 cubic inches. what is the radius of the baseball?

Explanation:

Step1: Recall the volume formula for a sphere

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

Step2: Substitute the given volume into the formula

Given \(V = 113.04\) cubic inches and \(\pi\approx3.14\), we substitute into \(V=\frac{4}{3}\pi r^{3}\):
\(113.04=\frac{4}{3}\times3.14\times r^{3}\)

Step3: Simplify the equation

First, calculate \(\frac{4}{3}\times3.14 = 4.1867\) (approx). Then the equation becomes \(113.04 = 4.1867r^{3}\).
Solve for \(r^{3}\): \(r^{3}=\frac{113.04}{4.1867}\approx27\)

Step4: Find the radius

Take the cube - root of \(r^{3}\). Since \(r^{3}=27\), then \(r = \sqrt[3]{27}=3\) inches.

Answer:

The radius of the baseball is \(3\) inches.