Question

An open-topped box is constructed from a square piece of cardboard by removing a square of size 4 inches from each corner and turning up the edges. If the box is to hold 2,116in 3

, how big should the originial piece of cardboard be?

Answer 1

31 inches square

Explanation:

You want to know the original size of a square piece of cardboard that forms an open box with volume 2116 in³ when a 4-in square is removed from each corner and the sides folded up.

Base

The volume of the box is given by ...

V = Bh

where B is the area of the bottom of the box, and h is its height. Solving for B, we have ...

B = V/h = (2116 in³)/(4 in) = 529 in²

Square

Since the base is square, its side length can be found from ...

B = s²

s = √B = √(529 in²) = 23 in

Each side of the box adds 4 inches to the base dimension, so the original square is 8 inches larger in both dimensions.

The original piece of cardboard is a square 31 inches on a side.

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