Cubic Feet Math Problem

Question

An open box is to be constructed from a square piece of sheet metal by removing a square of side 3 feet from each corner and turning up the edges. If the box is to hold 147 cubic ​feet, what should be the dimensions of the sheet​ metal?

Answer 1

Let S represent the side length of the square sheet metal. By cutting out 3-foot squares from each corner and folding the ends to form a box, we end up with a box of height 3 feet and a square base of side S-6 feet. The Volume of such an object is (Area of Base) * Height = (S-6)² * 3. We are told that the volume is 147 cu. ft. Thus, we have an equation to solve:

3(S-6)² = 147

(S-6)² = 147 / 3 = 49

S - 6 = ±7

S = 6 ± 7

S is either 13 or -1. We can eliminate -1 because lengths cannot be negative.

Thus, S = 13 feet.