Two conical paper funnels are similar in shape; the smaller stands 12 cm tall and the larger 18 cm. Covering the curved surface of the smaller one takes 48 cm² of foil. How many cm² of foil are needed for the larger one?

Question

Accepted Answer

108. The linear ratio is 18 : 12 = 3 : 2. Surfaces of similar solids grow as the square of that ratio, so the foil needed = 48 × (3/2)² = 48 × 9/4 = 108 cm². (Scaling by the linear ratio 1.5 gives 72 cm²; scaling by the cube 3.375, which belongs to volume, gives 162 cm²; 96 cm² just doubles.)

Two conical paper funnels are similar in shape; the smaller stands 12 cm tall and the larger 18 cm. Covering the curved surface of the smaller one takes $48 cm^{2}$ of foil. How many $cm^{2}$ of foil are needed for the larger one?

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Two conical paper funnels are similar in shape; the smaller stands 12 cm tall and the larger 18 cm. Covering the curved surface of the smaller one takes 48cm2 of foil. How many cm2 of foil are needed for the larger one?

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More Areas & Volumes practice

Two conical paper funnels are similar in shape; the smaller stands 12 cm tall and the larger 18 cm. Covering the curved surface of the smaller one takes $48 cm^{2}$ of foil. How many $cm^{2}$ of foil are needed for the larger one?