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?
The Answer is 33.6π mm2

Answer 1

Answer:

Lateral area of the smaller cylinder = 33.6 π mm²

Step-by-step explanation:

Circumference of the base of a cylinder is 24π mm . A similar cylinder has a base with circumference of 60π mm. Since we are dealing with the circumference of two similar cylinder we need to know the scale factor.

The square factor can be expressed as follow

Scale factor is the ratio between the larger circumference of the larger cylinder to the  circumference of the smaller cylinder.

Scale factor = 60π/24π  = 2.5

The lateral area of the larger cylinder = 210π mm².

The scale factor  squared is equal to the ratio of the larger cylinder surface area to the smaller cylinder  surface area.

Therefore,

2.5² = 210π/a

where

a = surface area of the smaller cylinder

cross multiply

6.25 a = 210π

divide both sides by 6.25

a = 210π/6.25

a = 33.6 π mm²

Lateral area of the smaller cylinder = 33.6 π mm²