A toy designer is creating a basketball plushy. The designer has fabric that measures 171.9 sq. in. What is the maximum radius of the basketball that the designer can create? Use 3.14 for π.Group of answer choices13.7 in6.9 in3.7 in3.4 in
Question
A toy designer is creating a basketball plushy. The designer has fabric that measures 171.9 sq. in. What is the maximum radius of the basketball that the designer can create? Use 3.14 for π.Group of answer choices13.7 in6.9 in3.7 in3.4 in
Solution
The formula for the surface area of a sphere (which is the shape of a basketball) is 4πr². We can use this formula to find the maximum radius of the basketball plushy that the designer can create.
Given that the fabric measures 171.9 sq. in., we can set up the equation:
4πr² = 171.9
Substitute 3.14 for π:
43.14r² = 171.9
Solve for r²:
r² = 171.9 / (4*3.14)
r² = 13.7
Then, take the square root of both sides to solve for r:
r = √13.7
So, the maximum radius of the basketball that the designer can create is approximately 3.7 inches. Therefore, the correct answer is 3.7 in.
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