Question

part d
question
the volume of a soccer ball is about 371 cubic inches.
use this information and the equation modeling the radius of the soccer ball to complete this statement. use 3.14 for π.
the radius of the soccer ball, rounded to the nearest tenth of an inch, is
inches.

Explanation:

Step1: Recall the volume formula for a sphere

The volume formula for a sphere is \(V = \frac{4}{3}\pi r^{3}\). We know that \(V = 371\) and \(\pi\approx3.14\).

Step2: Substitute the values into the formula

Substitute \(V = 371\) and \(\pi = 3.14\) into \(V=\frac{4}{3}\pi r^{3}\), we get \(371=\frac{4}{3}\times3.14\times r^{3}\).
First, simplify the right - hand side: \(\frac{4}{3}\times3.14=\frac{12.56}{3}\approx4.19\). So the equation becomes \(371\approx4.19r^{3}\).
Then, solve for \(r^{3}\): \(r^{3}=\frac{371}{4.19}\approx88.54\).

Step3: Find the value of \(r\)

Take the cube root of both sides. \(r=\sqrt[3]{88.54}\). Using a calculator, \(r\approx4.46\approx4.5\) (rounded to the nearest tenth).

Answer:

\(4.5\)