problem solving question

Stuck on this question, I think i have to differentiate something but am struggling to form an equation. Help appreciated!

A rectangular sheet of cardboard measures 24 cm by 15 cm. Equal squares of side x cm are removed from each corner of the rectangle. The edges are then turned up to make an open box of volume V cm^3.

Find the maximum possible volume of the box and the corresponding value of x.

Another hint. x cannot be greater than 7.5, or less than 0. Can you see why?

Than value of x for which the volumes is maximised is an integer, so, check your working if you don't get one.

Ok so i got an expression for V
V=((24-2x)(15-2x))*(15+x)
Is this correct?

Almost. Check the height of the box.

Idk about the height, here is my sketch though. Cant really visualise it

Draw the flat rectangle, with the corners cut. Can you see the height now?

is it 15-2x

No. Imagine folding along the dotted lines:

Can you see what the height is now?