The surface area of a rectangular prism is 32 square inches. The volume of the prism is 12 cubic inches. The sum of all edge lengths is 28 inches. If the length width and height are increased by 1 inch, what is the volume?

36 cubic inches.

Step-by-step explanation:

Let the length, width and height of the rectangular prism are a, b, c respectively.

So, surface area, 2 (ab + bc + ca) = 32 {Given} ... (1)

Volume, abc = 12 {Given} ... (2)

And, the sum of all the edges, 4 (a + b + c) = 28 {Given} ... (3)

Now, if the length width and height are increased by 1 inch, then the volume of the prism will be = (a + 1) (b + 1) (c + 1)

= abc + (ab + bc + ca) + (a + b + c) + 1

= 12 + 16 + 7 + 1 {From equations (1), (2) and (3) }

= 36 cubic inches. (Answer)