The ratio of the diameters of two similar cylinders is 3:5. if the surface area of the smaller cylinder is 378 square inches, find the surface area of the larger cylinder.

Answer 1

Let the radii of the smaller and the larger cylinders be r and R respectively.

Also, let their heights be h and H respectively.

The ratio of the diameters of two similar cylinders is 3:5

r : R = 3 : 5

R = 5r/3

Also, the cylinders are similar.

Therefore h : H = r : R = 3 : 5

H = 5h/3

The surface area of the smaller cylinder is s = π r² + π r² + 2π r h = 378

and the surface area of the larger cylinder is

π R² + π R² + 2π R H

= π (5r/3)² + π (5r/3)² + 2π (5r/3) (5h/3)

= (25/9)π r² + (25/9)π r² + (25/9)2π r h

= (25/9) × [π r² + π r² + 2π r h]

= (25 ÷ 9) × 378 = 1050 square inches