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?

Question

How would I write an equation for this problem and solve it? I am in 8th grade and doing Honors level math. Thank you!

Answer 1

The question is stating that the out side of the metal box is 12 inches in length. Since it's cubic, then the height and width are also 12 inches. Since the metal walls are 3 inches thick, you can solve for this problem by subtracting the volume of the empty space inside from the volume of the outside of the box.

 

the outside dimension is 12, the inside length is 12 - 3 = 9 inches;

 

length = width = height = x;

Box volume(x) = x^3

Box volume(outside length) - Box volume(inside length) = (12 inches)^3 - (9 inches) ^ 3 = 1728 - 729 inches^3 = 999 inches^3

 

I hope this helps!