Question

A box is to be made from a rectangular sheet of cardboard 70cm by 150cm by
cutting equal squares out of the four corners and bending four flaps to make
the sides of the box. (The box has no top.) What is the largest possible
volume of the box?

Answer 1

if a square with side of length x cm is cut from each of the 4 corners and the flaps folded you get a rectangular box with sides x,70-2x,150-2x.
Volume of the box=x(70-2x)(150-2x)=4x^3-440x^2+10500x
Volume is maximum when the derivative =0
dV/dx=0
dV/dx= 12x^2-880x+10500=0
Solve the quadratic and get the value of x