Question
Two cylinders have the same volume, but the radius of
the base of the second cylinder is 20% less than the radius of the base of the first. How much greater should the height of the second cylinder be in comparison to the height of the first?Solution
Let the radius of the first cylinder be R. Now, the radius of the base of the second cylinder =R-Rx 20% =R-0.2R =0.8R Let height of the first and second cylinder be H ₁ and H ₂ respectively. According to the question, π x R2 x H ₁ = 1 x (0.8R)2 x H2 R2 x H ₁ = 0.64R2 x H2 H ₁ = 0.64H2 Now, % greater = (H2- 0.64H2)/0.64H2 × 100% =0.36/0.64 × 100% =56.25% 56.25% greater the height of the second cylinder should be in comparison to the height of the first.
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