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Question

If the radius of a right circular cylinder open at both the ends, is decreased by 25% and the height of the cylinder is increased by 25%. Then the curved surface area of the cylinder thus formed

A remains unaltered Correct Answer Incorrect Answer
B is increased by 25% Correct Answer Incorrect Answer
C is increased by 6.25% Correct Answer Incorrect Answer
D is decreased by 6.25% Correct Answer Incorrect Answer

Solution

Curved suface area of cylinder = 2 πrh
New radius of the cylinder = r × (75/100) = 0.75r
New height of the cylinder = h × (125/100) = 1.25h
Curved surface area of new cylinder = 2 π × 0.75r × 1.25h
Taking ratio of C.S.A before to after = 2 πrh : 2 π × 0.75r × 1.25h = 1 : 0.9375
Let C.S.A before be 1 and after C.S.A be 0.9375
C.S.A decrased by = 1 – 0.9375 = 0.0625
∴ C.S.A decresed by (in %) = 0.0625/1 × 100 = 6.25%

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