9514 1404 393
Answer:
1816.7 in³ ≈ 29,769.6 cm³
Explanation:
The surface area of a sphere is given by the formula ...
A = 4πr²
Then the radius is ...
r = √(A/4π) = (1/2)√(A/π)
The volume of a sphere is given by the formula ...
V = 4/3πr³
Using the above value of r, we find the volume to be ...
V = (4/3)π(1/2)³(A/π)^(3/2) = 1/6√(A³/π) ≈ 1816.7 in³
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The answer is requested in cm³. The conversion factor is (2.54 cm/(1 in))³, so this volume is ...
(1816.7 in³)·(2.54 cm/(1 in))³ = 29,769.6 cm³
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Additional comment
We suspect an error in the problem statement, as the given units are square inches and the requested volume is in cubic centimeters. Usually, there would be an explicit statement regarding the necessity for units conversion.