Question

A closed box has a square base with side length l feet and height h feet. Given that the volume of the box is 35 cubic feet, express the surface area of the box in terms of l only. ??

Answer 1

`A = (2(70+I^3))/I`

Explanation:

So we are told that the box has a square base, so all four sides are the same length I.

Volume = Length x Breadth x Height

So we know that Length and Breadth are both equal to I. Hence

`35 = I*I*h`

`implies h = 35/I^2`

Now we need to calculate the surface are of the box. There are four side faces with area `I*h` as well as a top and bottom face of area `I^2`. Therefore

`A = 4(I*h) + 2I^2`

`A = 4I*35/I^2 + 2I^2`

`A = 140/I + 2I^2`

`A = (2(70+I^3))/I`