Question

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.

Explanation:

Step1: Recall the formula for the surface area of a sphere

The formula for the surface area \( S \) of a sphere is \( S = 4\pi r^2 \), where \( r \) is the radius of the sphere.

Step2: Substitute the given surface area into the formula

We know that \( S = 320 \) square centimeters. So we set up the equation:
\( 320 = 4\pi r^2 \)

Step3: Solve for \( r^2 \)

First, divide both sides of the equation by \( 4\pi \):
\( r^2=\frac{320}{4\pi}=\frac{80}{\pi} \)

Step4: Solve for \( r \)

Take the square root of both sides. Since radius is a positive quantity, we consider the positive square root:
\( r = \sqrt{\frac{80}{\pi}} \)
Now, calculate the value. We know that \( \pi\approx3.14159 \), so:
\( \frac{80}{\pi}\approx\frac{80}{3.14159}\approx25.4648 \)
Then \( r=\sqrt{25.4648}\approx5.05 \) (rounded to two decimal places)

Answer:

5.05