The circumference of the base of a cylinder is 242 mm. A similar cylinder has a base with circumference of 60 mm. The

lateral area of the larger cylinder is 210 mm?

What is the lateral area of the smaller cylinder?

17.17 mm

33.67 mm

60x mm?

847 mm?

33.6π mm²

Step-by-step explanation:

The ratio of areas between two similar shapes is the square of the ratio of the lengths of the shapes.

A₁ / A₂ = (L₁ / L₂) ²

Given that A₂ = 210π mm², L₁ = 24π mm, and L₂ = 60π mm:

A₁ / 210π = (24π / 60π) ²

A₁ = 210π (24π / 60π) ²

A₁ = 33.6π

The area of the smaller cylinder is 33.6π mm².