Hello, mathsB!

I have no idea what a "net" is . . .

Consider a rectangle of perimeter 60Cm.

Form a cylinder by revolving this rectangle about one of its edges.

What dimensions of the rectangle will result in a cylinder of maximum **volume**?

(Include a net of the final shape) We have a rectangle with dimensions $\displaystyle L \times W$. Code:

* - - - - - *
| |
W | |
| |
* - - - - - *
L

The perimeter is 60 cm: .$\displaystyle 2L + 2W \:=\:60\quad\Rightarrow\quad W \:=\:30 - L$ .**[1]**

Revolve the rectangle about a vertical side.

The cylinder has radius $\displaystyle L$ and height $\displaystyle W$.

. . It volume is: .$\displaystyle V \:=\:\pi r^2h \:=\:\pi L^2W$. . **[2]**

Substitute [1] into [2]: .$\displaystyle V \;=\;\pi L^2(30-L)$

Now maximize this function.

. . $\displaystyle \text{(I got: }L = 20,\;W = 10)$