Problema Solution
A box can be made by cutting out the corners and folding up the edges of a sheet of cardboard. A template for a cardboard box with a height of 2 inches is given. What is the length of each side of the cardboard sheet if the volume of the box is to be 50 cubic inches?
Answer provided by our tutors
we will assume the cardboard sheet is a square and 'a' represents the length of each side of the cardboard sheet, a>0
V = 50 in^3 the volume of the box
h = 2 in the height of the box
(a - 2h) = the length of the base of the box
V = (a - 2h)^2*h
(a-2*2)^2*2 = 50
by solving we find:
a = 9 in
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the length of the side of the cardboard sheet is 9 inches.