Question

if 1000 square cm of materials is available to make a box with a square base and a closed top, find the dimensions of the box that will have the largest possible volume.

Answer 1

Assume the side of square base = x
and height of the box to be y

Volume V = x * x * y = x^2y ----- (1)

Find the total surface area of the box and set it to 1000. ------ (2)

Find y in terms of x from the second equation and put it in (1)

Find dV/dx, set it to 0 and solve for x.