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Answer :
Answer:
[tex]A=502.4\ \text{inches}^2[/tex]
Step-by-step explanation:
The radius of the ball, r = 2 inches
We need to find how many square inches of plastic does the company need to make 10 beach balls.
Let A be the area of 1 ball. Balls are in the form of spheres. The area of a sphere is given by :
[tex]A=4\pi r^2[/tex]
For 10 balls,
[tex]A=10\times 4\pi r^2\\\\=10\times 4 \times 3.14\times (2)^2\\\\=502.4\ \text{inches}^2[/tex]
Hence, the area of 10 beach balls is [tex]502.4\ \text{inches}^2[/tex].
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Rewritten by : Barada
Final answer:
To make 10 beach balls, each with a radius of 2 inches, a company would need 502.4 square inches of plastic when rounded to the nearest tenth.
Explanation:
The question asks how much plastic is needed to make 10 beach balls with a radius of 2 inches each. To find the surface area of one beach ball, we use the formula for the surface area of a sphere, which is SA = 4πr². Substituting 3.14 for π (pi) and 2 inches for the radius (r), we calculate the surface area of one ball and then multiply by 10 to find the total amount needed for ten balls.
First, calculate the surface area of one ball: SA = 4 × 3.14 × (2 inches)². Simplify to get SA = 4 × 3.14 × 4 inches² = 50.24 inches². Now, multiply the surface area of one ball by 10 to find the total surface area for 10 balls: 50.24 inches² × 10 = 502.4 inches².
