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]

To solve the problem, we start by finding the surface area of one beach ball using the formula

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

Given that the radius is [tex]$r = 2$[/tex] inches and using [tex]$\pi = 3.14$[/tex], we substitute these values into the formula:

[tex]$$
SA = 4 \times 3.14 \times (2)^2.
$$[/tex]

First, calculate [tex]$(2)^2$[/tex]:

[tex]$$
(2)^2 = 4.
$$[/tex]

Then, substitute back into the equation:

[tex]$$
SA = 4 \times 3.14 \times 4.
$$[/tex]

Multiply these numbers together:

[tex]$$
SA = 50.24 \text{ square inches}.
$$[/tex]

This is the surface area of one beach ball. Since the company makes [tex]$10$[/tex] beach balls, the total surface area required is:

[tex]$$
\text{Total Surface Area} = 10 \times 50.24 = 502.4 \text{ square inches}.
$$[/tex]

Thus, the company needs approximately

[tex]$$
502.4 \text{ in}^2
$$[/tex]

of plastic to make [tex]$10$[/tex] beach balls.