Two boxes are similar in shape, one being a scale model of the other, and the ratio of their volumes is 8 : 125. Wrapping the smaller box completely takes 96 cm² of paper. How many cm² of paper are needed to wrap the larger box completely?

Question

Accepted Answer

600. Volumes are in the ratio of the cubes of corresponding lengths, so the linear ratio = ∛8 : ∛125 = 2 : 5. Surface areas are in the ratio of the squares, 4 : 25. Paper needed = 96 × 25/4 = 600 cm².

Two boxes are similar in shape, one being a scale model of the other, and the ratio of their volumes is 8 : 125. Wrapping the smaller box completely takes $96 cm^{2}$ of paper. How many $cm^{2}$ of paper are needed to wrap the larger box completely?

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Two boxes are similar in shape, one being a scale model of the other, and the ratio of their volumes is 8 : 125. Wrapping the smaller box completely takes 96cm2 of paper. How many cm2 of paper are needed to wrap the larger box completely?

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Areas & Volumes practice

Two boxes are similar in shape, one being a scale model of the other, and the ratio of their volumes is 8 : 125. Wrapping the smaller box completely takes $96 cm^{2}$ of paper. How many $cm^{2}$ of paper are needed to wrap the larger box completely?