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, 2014

Algebra Difficulty 2.6 Junior Find the answer Canada

A cube has an edge length of 30. A rectangular solid has edge lengths 20, 30 and $L$ . If the cube and the rectangular solid have equal surface areas, what is the value of $L$ ?

Pick one

Solution

The cube has six identical square faces, each of which is 30 by 30.

Therefore, the surface area of the cube is $6(30^2) = 5400$ .

The rectangular solid has two faces that are 20 by 30, two faces that are 20 by $L$ , and two faces that are 30 by $L$ .

Thus, the surface area of the rectangular solid is $2(20)(30) + 2(20L) + 2(30L) = 100L + 1200$ .

Since the surface areas of the two solids are equal, then $100L + 1200 = 5400$ or $100L = 4200$ , and so $L=42$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.