Question

An open box is to be made from a ft by ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.

Answer 1

432 cm
`^(3)`

Explanation:

The volume of the box can be determine by using derivative function:

V = (18 - 2x) (18 - 2x) x

dV/dx = 4x^3 + 324 + 144x

equating to zero;

(x - 9) (x - 3) = 0

x = 9 , 3

putting the values in the equation;

V = (18 - 2 [3]) (18 - 2[3]) 3

volume = 432.