Two cylinders of volume 64 cm^3 and 8 cm^3 are similar. If the surface area of the larger cylinder is 90 cm^2 , find the surface area of the smaller one.

Question

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Answer 1

The ratio of the volume of the two cylinders V1: V2 -> r1³ : r2³

64: 8 -> 4³ : 2³

The ratio of the raidus 1 and radius 2 is r1: r2 = 4: 2

The ratio of the surface area is A1: A2 is r1² : r2² -> 4² : 2² So the area ratio is 16: 4 or 4:1

Smaller SA / 90 = 1 / 4

Smaller SA = 1/4 * 90 = 22.5 cm²