Question

Find the volume of the sphere that has a surface area of 720 in2. Round your answer to the nearest tenth.

Answer 1

9514 1404 393

Answer:

  1816.7 in³ ≈ 29,769.6 cm³

Step-by-step 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.