Question

A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in. squares from each corner and folding up the sides. The box is to hold 12943 in3. How big a piece of cardboard is needed?

Answer 1

The size of the cardboard should be 30.5 in approximately from each side.

Explanation:

Given:

volume of the box = 12943 in³

Box cover size = 7 in

Size of the cardboard needed = ?

Since the base of the box is in the shape of a square, the box would be a cube.

So,

volume of box = (side)³

12943 in³ = (a)³

$a = \sqrt[3]{12943} \\\\a = 23.48in$

7 inch from all the sides of the cardboard will be cut and folded.

Therefore, size of the cardboard should be 23.48 in + 7 in

size = 30.48 in.