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Question

if the radius of a cylinder is increased by 10% by how much percent its height would decrease if the curved surface area of cylinder remains the same?

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Solution

Let the original radius of base of cylinder = rLet the original height of cylinder = hOriginal CSA = 2πrhLet r' be the new radius and h' be the new height of cylinder.Now, r' = r + 10% of r = r + 10100×r = r + r10 = 11r10Let m% be the decrease in height.Now, h' = h - m% of h = h - m100×h = h100-m100Now, new CSA = 2πr'h' = 2π11r10 × h100-m100Now, original CSA = new CSA 2πrh = 2π11r10 × h100-m100 100-m100 = 10111100-11m = 100011m = 100m = 10011% = 9111%

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