The formula for the area of a sphere is ...
... A = 4πr²
Solving for r gives
... r = √(A/(4π)) = (1/2)√(A/π)
The formula for the volume of a sphere is ...
... V = (4/3)πr³
Comparing this to the area formula, we see that ...
... V = A·(r/3)
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a) Scale factor = √(area ratio) = √(100π/(36π)) = 10/6 = 5/3
... The larger sphere is 5/3 the dimensions of the smaller sphere.
b) Radius of the smaller sphere is
... (1/2)√(36π/π) = 3 . . . units
c) Radius of the larger sphere is
... (1/2)√(100π/π) = 5 . . . units . . . . = (5/3)·3 units
d) Volume of the smaller sphere is
... V = A·r/3 = (36π)·(3/3) = 36π . . . units³
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e) Volume of the larger sphere is
... V = A·r/3 = (100π)·(5/3) = 500π/3 . . . units³