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Answer :
To find out how many square inches of plastic the company needs to make 10 beach balls, we need to calculate the surface area of one beach ball first and then multiply that by 10.
Here’s a step-by-step breakdown:
1. Identify the formula: The formula to calculate the surface area of a sphere (which is the shape of a beach ball) is:
[tex]\[
SA = 4 \pi r^2
\][/tex]
2. Given values:
- The radius ([tex]\( r \)[/tex]) of each beach ball is 2 inches.
- Use [tex]\( \pi = 3.14 \)[/tex].
3. Calculate the surface area of one beach ball:
[tex]\[
SA = 4 \times 3.14 \times (2)^2
\][/tex]
[tex]\[
SA = 4 \times 3.14 \times 4
\][/tex]
[tex]\[
SA = 50.24 \quad \text{square inches}
\][/tex]
4. Calculate the total surface area needed for 10 beach balls:
[tex]\[
\text{Total surface area} = 50.24 \times 10
\][/tex]
[tex]\[
\text{Total surface area} = 502.4 \quad \text{square inches}
\][/tex]
Therefore, the company needs 502.4 square inches of plastic to make 10 beach balls. The correct answer is 502.4 in².
Here’s a step-by-step breakdown:
1. Identify the formula: The formula to calculate the surface area of a sphere (which is the shape of a beach ball) is:
[tex]\[
SA = 4 \pi r^2
\][/tex]
2. Given values:
- The radius ([tex]\( r \)[/tex]) of each beach ball is 2 inches.
- Use [tex]\( \pi = 3.14 \)[/tex].
3. Calculate the surface area of one beach ball:
[tex]\[
SA = 4 \times 3.14 \times (2)^2
\][/tex]
[tex]\[
SA = 4 \times 3.14 \times 4
\][/tex]
[tex]\[
SA = 50.24 \quad \text{square inches}
\][/tex]
4. Calculate the total surface area needed for 10 beach balls:
[tex]\[
\text{Total surface area} = 50.24 \times 10
\][/tex]
[tex]\[
\text{Total surface area} = 502.4 \quad \text{square inches}
\][/tex]
Therefore, the company needs 502.4 square inches of plastic to make 10 beach balls. The correct answer is 502.4 in².
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