The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces.

Let the radius of the first cylinder be 2x and the second cylinder is 3x. 

The height of the first cylinder be 5y and the second cylinder is 3y. 

The volume of the first cylinder is = π (2 * x)2 * 5 * y   

The volume of the first cylinder is =  π (3 * x)2 * 3 * y

Ratio = [π (2 * x)2 * 5 * y] / [π (3 * x)2 * 3 * y]

= 20 / 27 

Ratio of radius of two cylinder, r1 : r2 = 2:3 

Ratio of their heights, h1 : h2 = 5 : 3 

r1 / r2 = 2 / 3 

h1 / h2  = 5 / 3 

Curved surface area of cylinder 1 / curved surface area of cylinder 2 

= 2πr1h1 / 2πr2h2 

= (2 × 22 / 7 × 2 × 5) / (2 × 22 / 7 × 3 × 3) 

= 10 / 9

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