Question 547141: find the volume of a spherewhose surface areais 616sq cm
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! As with squares (area) and perimeters (linear distance) and cubes (volume) and their planar surfaces (area), where there are tighly coupled relationships between the formulae for their respective computations, spheres (volume) and their surfaces (area) use the same driver, the radius, r, which can be given or derived.
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Surface area of a sphere: A = 4 Pi * r^2
Interior volume of a sphere: V = 4/3 Pi * r^3
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Clearly r is important to both.
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Given:
A = 616 sq cm
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Find:
V = ?
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Since r is part of both equations, we can back into r from the given A, and then compute the volume, V:
A = 4 Pi r^2 can be rewritten in terms of r:
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divide both sides by 4 Pi:
A / (4 Pi) = r^2
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take square root of both sides:
r = Sqrt(A/(4Pi))
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r = Sqrt(616/(4 * Pi)
r = 7.0014 cm
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take this r and insert it into the equation for V:
V = 4/3 Pi 7.0014^3
V = 1,437.62 cu cm
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cheers,
Lee
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