A company makes plastic beach balls with a radius of 2 inches. How many square inches of plastic does the company need to make 10 beach balls? Use 3.14 for [tex]$\pi$[/tex] and round to the nearest tenth.

Recall the formula [tex]$SA = 4\pi r^2$[/tex].

A. 50.24 in.[tex]$^2$[/tex]
B. 100.5 in.[tex]$^2$[/tex]
C. 251.2 in.[tex]$^2$[/tex]
D. 502.4 in.[tex]$^2$[/tex]

Sure! Let's go through solving the problem step by step.

1. Understand the Problem:
We need to find out how many square inches of plastic are required to make 10 plastic beach balls if each ball has a radius of 2 inches. We will use the surface area formula for a sphere: [tex]$ SA = 4 \pi r^2 $[/tex].

2. Identify the Given Values:
- Radius ([tex]$ r $[/tex]) = 2 inches
- Number of beach balls = 10
- Use [tex]$ \pi = 3.14 $[/tex] as provided.

3. Calculate the Surface Area of One Beach Ball:
The formula for the surface area of a sphere is:
[tex]\[
SA = 4 \pi r^2
\][/tex]
Substituting the given values:
[tex]\[
SA = 4 \times 3.14 \times (2)^2
\][/tex]
[tex]\[
SA = 4 \times 3.14 \times 4
\][/tex]
[tex]\[
SA = 50.24 \, \text{square inches}
\][/tex]

4. Calculate the Total Surface Area for 10 Beach Balls:
Multiply the surface area of one beach ball by the number of beach balls:
[tex]\[
\text{Total Surface Area} = 50.24 \times 10 = 502.4 \, \text{square inches}
\][/tex]

5. Conclusion:
The company needs 502.4 square inches of plastic to make 10 beach balls.

Therefore, the correct answer is 502.4 in², which corresponds to the last option in the list.