Question

We can use the formula r=radical S/12.6 to relate a ball's surface area S (in square inches) to its radius r (in inches). Suppose a ball has a surface area of 176.4 square inches. What is its radius?Round your answer to the nearest tenth.

Answer 1

Using the given formula with the value of S = 176.4 in², let's calculate the value of r:

$\begin{gathered} S=4\pi r^2\to r=\sqrt[]{\frac{S}{4\pi}}=\sqrt[]{\frac{S}{12.6}} \\ \\ r=\sqrt[]{\frac{176.4}{12.6}} \\ r=\sqrt[]{14} \\ r=3.7 \end{gathered}$

So the ball radius is 3.7 inches.