Question
The radius of a cylinder is increased by 20%, and its
height is decreased by 10%. Find the percentage change in the volume of the cylinder.Solution
Let the initial radius be r and height be h. The initial volume is: V₁ = πr²h. New radius = 1.2r, new height = 0.9h. New volume: V₂ = π(1.2r)²(0.9h) = π(1.44r²)(0.9h) = πr²h × 1.296. Percentage change in volume: [(V₂ - V₁)/V₁] × 100 = [(1.296V₁ - V₁)/V₁] × 100 = 29.6%. Correct answer: c. 29.6% increase
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