Just want to make sure im doing it correct! a Rectangle sheet of perimeter 36cm with dimensions x (vertical) and y (horizontal) is to be rolled into a cylinder where x= height and y= circumference. what values of x and y will give largest volume? Write volume in terms of only one variable "y" when solving. So volume of cylinder: V=2(pi)r*h when applying our variables: V= y * x y= 2(pi)r x=h This I know is our primary equation: v=y*x for the cylinder Now they gave us the perimeter which must be 36cm...so our 2nd equation will be the perimeter of the rectangle before its rolled up into a cylinder: P=2x+2y p=36 So i got (in terms of y): 36=2x+2y 18-y=x Using this i applied what x equaled in our 2nd equation to our primary equation: V=y* (18-y) I then took the derivative and got Dv/dt= 18-2y I then solved for a critical point (making the derivative equal 0) and got y=9. making my values to be y=9cm x=9cm Does this seem right? Also would my domain be from (0,36)?