Question

How much metal is needed to smelt a cubical metal box with outer side 12 inches long if the thickness of its walls should be exactly 3 inches?

Answer 1

Answer: 1,512 cubic inches

Step-by-step explanation:

To get the length of the inner side of the cube, we multiply the thickness by 2 and then, we subtract the result from the outer side of the cube.

In terms of equation:

(inner side) = (outer side) - 2(thickness)

Since the outer side is 12 inches and the thickness is 3 inches, then the inner side is given by

(inner side) = (outer side) - 2(thickness)
= 12 - 2(3)
(inner side) = 6 inches

Therefore, the amount of metal needed to smelt the cubic box is given by

(Volume of metal) = (outer side)³ - (inner side)³
= 12³ - 6³
= 1,728 - 216
= 1,512 cubic inches