Problema Solution
An open rectangular box with length four times its width is made from a rectangular piece of metal by cutting a 2 cm square from each corner and turning up the sides. If the volume of the box is 128 cm(cubed), find the dimensions of the original piece of metal.
Answer provided by our tutors
Let w be the width of the box.
Then 4w is the length of the box
The height of the box is 2 cm.
The volume of the box is: 2(4w)w = 8w^2 = 128
Divide by 8:
w^2 = 16
Take the square root, neglecting the negative root:
w = 4 cm
length = 4(4) = 16 cm
The original piece of metal was 4 + 2 + 2 cm x 16 + 2 + 2 cm =
8 x 20 cm