type the correct answer in the box. use numerals instead of words. the surface area of a sphere is 320…

type the correct answer in the box. use numerals instead of words. the surface area of a sphere is 320 square centimeters. what is the radius of the sphere? round your answer to 2 decimals places. the radius is centimeters.

type the correct answer in the box. use numerals instead of words. the surface area of a sphere is 320 square centimeters. what is the radius of the sphere? round your answer to 2 decimals places. the radius is centimeters.

Answer

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a sphere is $A = 4\pi r^{2}$, where $A$ is the surface area and $r$ is the radius. Given $A = 320$ square centimeters, we have the equation $320=4\pi r^{2}$.

Step2: Solve for $r^{2}$

First, divide both sides of the equation $320 = 4\pi r^{2}$ by $4\pi$. So, $r^{2}=\frac{320}{4\pi}=\frac{80}{\pi}$.

Step3: Solve for $r$

Take the square - root of both sides: $r=\sqrt{\frac{80}{\pi}}$. Using $\pi\approx3.14159$, we get $r=\sqrt{\frac{80}{3.14159}}\approx\sqrt{25.46479}\approx5.05$.

Answer:

$5.05$