Question

A rectangular sheet of perimeter 24 cm and dimensions x cm by y cm is to be rolled into a cylinder. what values of x and y give the largest volume?

Answer 1

because the perimeter is 36, we know that 2x+2y=36. Therefore y=18-x. If you take your sheet of paper, and roll it into a cylinder, y becomes the height. The volume of a cylinder is V=pi(r^2)h. However, you need to find the radius as well. When you rolled your rectangle up, x became the circumference. The formula for Circumference is C=2pi(r) so if x=C, then x=2pi(r). Does this help? I'm not gonna give you the answer straight up :)