Question

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.

What is the lateral area of the smaller cylinder?

17.1π mm2
33.6π mm2
60π mm2
84π mm2

Answer 1

Circumference = 2πr, so r_small = 24π/(2π) = 12 mm and r_large = 60π/(2π) = 30 mm. Linear scale factor small:large = 12/30 = 2/5, so area scale = (2/5)^2 = 4/25.

Lateral area_small = (4/25) × 210π = 840/25 π = 33.6π mm^2.

Answer: 33.6π mm^2.