Multiple choice

If two cubes of equal volume are to be made from rectangular block of volume $250$ cubic inches, then the combined surface area of the two cubes is greater than the surface area of the original rectangular block by $x$ square inches. Find the value of $x$.

  1. $50$
  2. $75$
  3. $25$
  4. $45$
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A Correct answer
AI explanation

The rectangular block has a volume of 250 cubic inches, and when divided into two equal cubes, each cube has a volume of 125 cubic inches. This means the edge length of each cube is the cube root of 125, which is 5 inches, making the surface area of one cube 6 times 5 squared, or 150 square inches. The combined surface area of both cubes is 300 square inches. Since the original rectangular block must have had dimensions of 5 by 5 by 10 inches to yield these cubes, its surface area was 2 times (5 times 5 plus 5 times 10 plus 5 times 10), or 250 square inches. The difference between the combined cube area and the original block area is 300 minus 250, which equals 50.

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