1.67: x cm x cm Diagram accurately dra

Figure cut form away an open shows from box. each a rectangular corner of sheet the sheet. of metal The sheet by is then folded A square along of the side dotted lines is to

The volume of the box is $\displaystyle V\mathrm{cm}^{3}$

(a) Show that $\displaystyle V = 4x3 - 52x2 + 160x$

(b) Using value of calculus, gives find a maximum the value value of for of which $\displaystyle V$ is a maximum, justifying that this

(c) Find the maximum value of $\displaystyle {\cal{V}}.$