Question

type the correct answer in the box. use numerals instead of words. helen needs a replacement ball bearing for this part. the surface area of each spherical ball bearing is approximately 452.16 square millimeters. what is the radius of the bearing that helen needs to buy? round your answer to a whole number. the replacement bearing has a radius of about \boxed{} millimeters.

Explanation:

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

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

Step2: Substitute the given surface area into the formula

We know that \( S = 452.16 \) square millimeters. So we set up the equation:
\[
4\pi r^2 = 452.16
\]

Step3: Solve for \( r^2 \)

First, divide both sides of the equation by \( 4\pi \). Let's use \( \pi \approx 3.14 \):
\[
r^2 = \frac{452.16}{4 \times 3.14}
\]
Calculate the denominator: \( 4 \times 3.14 = 12.56 \)
Then, \( r^2 = \frac{452.16}{12.56} = 36 \)

Step4: Solve for \( r \)

Take the square root of both sides:
\[
r = \sqrt{36} = 6
\]

Answer:

6