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14 Jan 2025, 09:14
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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The large rectangular solid shown here is formed by binding together nine identical rectangular rods, as shown.
Quantity A
Four times the surface area of just one of the identical rectangular rods
Quantity B
The surface area of the large rectangular solid above
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17 Jan 2025, 09:05
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OE
A rectangular solid has three pairs of opposing equal faces, each pair representing two of the dimensions of the solid (length × width; length × height; height × width). The total surface area of a rectangular solid is the sum of the surface areas of those three pairs of opposing sides.
According to the diagram, the dimensions of each rod must be 1 × 1 × 6. So the surface area of one such rod is:
2(1 × 1) + 2(1 × 6) + 2(1 × 6) = 26 or 2[(1 × 1) + (1 × 6) + (1 × 6)] = 26
That is, one rod has a total surface area of 26, and four times this surface area is 4 × 26 = 104.
Quantity A
Four times the surface area of just one of the identical rectangular rods = 104
Quantity B
The surface area of the large rectangular solid above
The large rectangular solid has a total surface area of: 2(3 × 3) + 2(3 × 6) + 2(3 × 6), or 90.
Therefore, Quantity A is greater.
A rectangular solid has three pairs of opposing equal faces, each pair representing two of the dimensions of the solid (length × width; length × height; height × width). The total surface area of a rectangular solid is the sum of the surface areas of those three pairs of opposing sides.
According to the diagram, the dimensions of each rod must be 1 × 1 × 6. So the surface area of one such rod is:
2(1 × 1) + 2(1 × 6) + 2(1 × 6) = 26 or 2[(1 × 1) + (1 × 6) + (1 × 6)] = 26
That is, one rod has a total surface area of 26, and four times this surface area is 4 × 26 = 104.
Quantity A
Four times the surface area of just one of the identical rectangular rods = 104
Quantity B
The surface area of the large rectangular solid above
The large rectangular solid has a total surface area of: 2(3 × 3) + 2(3 × 6) + 2(3 × 6), or 90.
Therefore, Quantity A is greater.
