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Answer :
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.
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.
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