Question
The radius of a sphere is 75% of the radius of a
cylinder, while the height of the cylinder is 25% greater than its radius. Determine the ratio of the volume of the sphere to that of the cylinder.Solution
Let the radius of the cylinder be '4a' units. So, the height of the cylinder = 4a X (5/4) = '5a' units Radius of the sphere = 4a X 0.75 = '3a' units Volume of the sphere = (4/3) X π X radius3 Volume of the cylinder = π X radius2 X height Therefore, required ratio = ((4/3) X π X radius3) :(π X radius2 X height) = [(4/3) X π X (3a) 3]:[π X (4a) 2 X 5a] = 36:80 = 9:20
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