Problema Solution
A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in. squares out of each corner and folding up the sides. The box needs to hold 1000 in3. How big a piece of cardboard is needed?
Answer provided by our tutors
Let
x = the length of the side of the original square of cardboard, x>0
x - 2*6 = x - 12 the length of the sides of the box, x>12
h = 6 in the height of the box
V = 1000 in^3 the volume of the box
V = h(x - 12)^2
V = 6(x - 12)^2
6(x - 12)^2 = 1000
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x = 24.91 in
The length of a side of the original square of cardboard is 24.91 inches.