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30 Jan 2025, 10:25
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The figure here shows two wooden cubes joined to form a rectangular solid. If each cube has a surface area of 24, what is the surface area of the resulting rectangular solid?
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01 Feb 2025, 10:19
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OE
The surface area of a cube is 6 times the area of one face, therefore, each square face of each cube must have an area of 4. One face of each cube is lost when the two cubes are joined, so the total surface area of the figure will be the sum of the surface areas of both cubes minus the surface areas of the covered faces.
Each cube has surface area of 24, so the total surface area is 48. Subtract the surface area of each of the two touching (and thus nonexterior) faces: 48 - 2(4) = 40.
Alternatively, you could find that, because the surface area of one side of each cube is 4, the side length of each cube is 2. Thus, the length of the overall rectangular solid is 4, while its width is 2 and its height is 2. The surface area will now be equal to the sum of all six faces: 2(2 × 4) + 2(2 × 4) + 2(2 × 2) = 40.
The surface area of a cube is 6 times the area of one face, therefore, each square face of each cube must have an area of 4. One face of each cube is lost when the two cubes are joined, so the total surface area of the figure will be the sum of the surface areas of both cubes minus the surface areas of the covered faces.
Each cube has surface area of 24, so the total surface area is 48. Subtract the surface area of each of the two touching (and thus nonexterior) faces: 48 - 2(4) = 40.
Alternatively, you could find that, because the surface area of one side of each cube is 4, the side length of each cube is 2. Thus, the length of the overall rectangular solid is 4, while its width is 2 and its height is 2. The surface area will now be equal to the sum of all six faces: 2(2 × 4) + 2(2 × 4) + 2(2 × 2) = 40.
