Two cylinders have the radii of their bases in the ratio 4 : 5 and their heights are in the ratio 5 : 7. Find the ratio of their curved surface areas.

Question

Accepted Answer

The curved surface area (CSA) of a cylinder is given by the formula: CSA = 2 * π * r * h, where r is the radius and h is the height.

Given:
Ratio of radii = 4 : 5
Ratio of heights = 5 : 7

Let the radii be 4x and 5x, and the heights be 5y and 7y respectively.

Then, the ratio of their curved surface areas = (2 * π * 4x * 5y) : (2 * π * 5x * 7y)
= (4x * 5y) : (5x * 7y)
= (4 * 5) : (5 * 7)  [x and y cancel out]
= 20 : 35
= 4 : 7

Therefore, the ratio of their curved surface areas is 4 : 7.

Answer

Answer

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