Packaging is one important feature in producing quality products. A box designer needs to produce a package for a product in the shapes of the pyramid with a square base having a total volume of 200 cubic inches. The height of the package must be 4 inches less than the length of the base. Find the dimensions of the product.

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Answers

2015-08-17T11:38:17+08:00
Let X be the length of the base and X - 4 be the height. Since area of the base is equal to X^2, we get: V = (1/3)(X^2)(X - 4) --> 200 = (1/3)(X^2)(X - 4) --> 600 = (X^2)(X - 4) --> 0 = X^3 - 4X^2 - 600 --> X = -3, -3, 1, 10. Since we can't use -3 and 1 since it will result to a negative product if we use it in the equation, we use 10. So we have: height: 6 in, length and width of square base: 10 in. (10 in x 10 in x 6 in)
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