Question

a rectangular piece of paper, measuring 50cm by 30cm, has a small square of side length X cut from each corner. The flaps are then folded up to form an open box in the shape of a cuboid.

a.) show the volume V of the cuboid may be expressed as V= 1500x - 160X^2 + 4x^3

b.) find the value X such that the cuboid has a maximum volume

c.) find the maximum possible volume of the cuboid

Answer 1

a.) v = x (50 - 2 x)(30 - 2 x) = x (1500 - 160 x + 4 x^2)
... = 1500 x - 160 x^2 + 4 x^3

b.) max for the quadratic ... -b / 2a = 160 / (2 * 4) = 20

c.) plug 20 into the volume equation