Chapter 10.4, Problem 11P

The radius r of a sphere is given by $r=\sqrt{\frac{SA}{4\pi }}$

where SA represents the sphere’s surface area. If a sphere has a surface area of 531 in². what is the length of its radius? Use $\pi =3.14$.

Round to the nearest hundredth of an inch.

To determine

To find: the radius of the sphere when its surface area is $531\text{ in}{\text{.}}^2$ .

Answer to Problem 11P

The radius of the sphere is $6.50$ when its surface area is $531\text{ in}{\text{.}}^2$ .

Explanation of Solution

Given information:

The function is $r=\sqrt{\frac{SA}{4\pi }}$ .

Calculation: to find the solution, first substitute and then simplify,

  $\begin{array}{l}r=\sqrt{\frac{SA}{4\pi }}\\ r=\sqrt{\frac{531}{4\pi }}\text{ [substitute]}\\ r=\sqrt{42.27}\text{ [simplify]}\\ r=6.50\text{ [square root]}\end{array}$

Thus, The radius of the sphere is $6.50$ when its surface area is $531\text{ in}{\text{.}}^2$ .