A square sheet of card of side 15 cm is to be made into an open-top box by cutting equal squares of side x cm from each corner and folding up the sides.
a. (i) Show that the volume V(x) (in cm3) of the box is given by V(x)=x(15−2x)2.
b. (ii) Express V(x) as a cubic polynomial in standard form.
c. (iii) Calculate the volume of the box when x=3cm.