Question

what is the volume of a box that can be created from a sheet of metal that measures 12 inches by 30 inches assume there is no top to the box

Answer 1

Explanation:

Given that metal sheet is available with dimensions 12x30 inches.

Let x be the side of the square cut from all the four sides so that they can be folded to make open box.

The dimensions of the box would be 12-2x, 30-2x and x

Volume = V(x) =
`(12-2x)(30-2x)x\\=(360-84x+4x^2)x\\`

x can take only values upto 6 since at 6 the length =0

Let x =5

Then volume = 5(20)(2) =200 square inches.