Question

if 1200cm^2 of materiel is available to make box with a square base and an open top, find the largest volume possible of the box.

Answer 1

Let x be the edge length of one of the squares. Equate the area of 5 squares to 1200 and solve for x :\[5x^2=1200 \]\[x=4 \sqrt{15} \]\[V=x^3 =\left( 4 \sqrt{15}\right)^3=960 \sqrt{15}\text{ cm}^3 \]