reza is helping en shah to make a box without the top. the box is made by cutting away four squares from the corners of a 30cm square piece

Let the squares that are cut out each be x by x cm       0<x<15

Now the volume of the prism will be

$$\\V=(30-2x)*(30-2x)*x\\\\ V=x(900-120x+4x^2)\\\\ V=4x^3-120x^2+900x\\\\ \frac{dV}{dx}=12x^2-240x+900\\\\ \frac{d^2V}{dx^2}=24x-240\\\\ $Stationary points will occur when $\frac{dV}{dx}=0\\\ 12x^2-240x+900=0\\\\ x^2-20x+75=0\\\\ (x-5)(x-15)=0\\\\ x=5\qquad or \qquad x=15\\\\$$

$$\\When \;\;x=5\;\;\\\\ \frac{d^2V}{dx^2}=24*5-240<0\qquad Maximum \;\;at\;\; x=5\\\\ When \;\;x=15\;\;\\\\ $Volume is 0$\\\\ $So maximum volume occurs when x=5$\\\\ $Maximum volume $= V=(30-10)*(30-10)*5=2000cm^3\\\\$$