Packaging is one important feature in producing quality products. A box designer needs to produce a package for a product in the shape of a 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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The formula for looking for the volume of a square pyramid is s^2 \frac{h}{3} .

s²h/3 = 200
s²h = 600
s²(s-4) = 600
s³ - 4s² - 600 = 0
(s - 10)(s² + 6s + 60) = 0

The second factor s² + 6s + 60 would have factors (s + _ ) (s + _ ) where the blanks are not necessarily equal but are positive. This would mean that s would have a negative value so we do not take that. 

The only possible length of the square base is 10 inches. The height being 6 inches.
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