You have 240 cubic inches of clay with which to make a sculpture shaped as a rectangular prism. You want the width to be 4 inches less than the length and the height to be 2 inches more than 3 times the length. What should the dimensions of the sculpture be.

Question

Darryl Vaughn

Mathematics

21 November, 16:10

You have 240 cubic inches of clay with which to make a sculpture shaped as a rectangular prism. You want the width to be 4 inches less than the length and the height to be 2 inches more than 3 times the length. What should the dimensions of the sculpture be.

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Paco · Answer 1

Length=6, width=2, height=20. We can write a function to solve this problem. Suppose the length of the sculpture is x inches. Then the width is (x-4) inches, and the height (3x+2) inches. Their product is the volume of the clay: x * (x-4) * (3x+2) = 240. Solve the equation, the only real answer is 6, so the length is 6 inches. Width is 6-4=2, and height is 3*6+2=20.