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
