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.