Problema Solution
A square is cut out of each corner of a rectangle sheet of aluminum that is 30 cm by 90 cm. The sides are folded up to form a rectangular container with no top. The area of the bottom of the container is 1600cm^2. What are the dimensions of each cut out square? Find the volume of the container? (V= lwh)
Answer provided by our tutors
let
l = 90 cm the length of the side of the rectangle
w = 30 cm the width of the side of the rectangle
x = the length of the side of the square that us cut out, x>0, x<30 (the cut out part can not have length bigger then the width)
the area of the bottom of the container is 1600 cm^2
(l - 2x)(w - 2x) = 1600
(90 - 2x)(30 - 2x) = 1600
by solving we find and consider the solution that is less than 30
x = 5 cm
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the length of the side of the cut out square (the dimensions of the square) is 5 cm.
the container has height equal to the side of the cut out square that is h = 5 cm
the volume of the container is V = lwh
V = 90*30*5
V = 13,500 cm^3