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 cylinders are similar, so their corresponding lengths have a ratio of 24π ÷ 60π = 0.4. Lateral area scales by the square of the length ratio, so the smaller cylinder’s lateral area is 210π × (0.4)² = 33.6π mm². Therefore, the answer is 33.6π mm².

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