Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. then it was folded into an open-top box. find the original dimensions of the square piece of cardboard if the volume of this box is 144 cm3.

Question

Mathematics

Kaden

2 June, 10:50

Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. then it was folded into an open-top box. find the original dimensions of the square piece of cardboard if the volume of this box is 144 cm3.

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Felix Bradshaw · Answer 1

Suppose the length of the card board was x cm by x cm

After squares of 4cm was cut from the corner, the dimension for the box will be:

length = (x-8) cm

width = (x-8) cm

height=4 cm

thus the volume will be:

V=length*width*height

V=4 * (x-8) * (x-8) = 144

x²-16x+64=36

this can be simplified to form a quadratic equation given by:

x²-16x+28=0

solving the quadratic equation we get:

x=2 or x=14

Thus we conclude that the original dimensions was:

length=14 cm; width=14 cm