Question

A rectangular piece of cardboard has a length of 32 cm. Squares of 4cm on a side are cut out of each corner of the rectangle so that the remaining piece can be folded into an open-topped box. IF the volume of the box is 768 cubic cm, what is the area of the original piece of cardboard?

Answer 1

518 cm²

Explanation:

We are told the length is 32 cm from the question.

Now, if 4 cm squares are removed from the width sides, it means it will now be lesser by 4 + 4 = 8 cm.

This means that the height will be 4 cm.

If length is L and width is W.

This means if 4 cm is cut from both sides, length is now;

L - 8 = 32 - 8 = 24 and width is w - 8

Volume of a cube is;

V = Lwh

Thus, we have;

V = 24 × (w - 8) × 4

We are told the volume is 786 m³

Thus;

24 × (w - 8) × 4 = 786

96(w - 8) = 786

w - 8 = 786/96

w - 8 = 8.1875

w = 8 + 8.1875

w = 16.1875

Thus,area = lw = 32 × 16.1875 = 518 cm²