HELP: Maximum Volume of a Solid of Revolution??

[deniseewood_71088]

Can someone please help me with this problem...A rectangular sheet of perimeter 36 cm and dimensions x cm by y cm (with y being long side) is to be rolled into a cylinder....Find the x and y values that gives the cylinder the largest volume (the rectangular sheet is to be revolved about one of the sides of length y). Im so lost and confused!

 

[stapel]

Draw the sheet. Label the sides with "x" and "y". Write the perimeter formula, using these variables and the given perimeter value.

Solve the perimeter equation for one of the variables.

Relate the variables to the dimensions of the resulting cylinder. (One will be the circumference of the base. The other will be the height.) Use this information to form the "volume" equation.

Use the results from the second paragraph to substitute for the one variable. This gives you the volume equation in one variable only.

Maximize.

Eliz.

 

[galactus]

Here's another hint:

Since x=circumference, then \(\displaystyle x=2{\pi}r\), \(\displaystyle r=\frac{x}{2{\pi}}\)

Height=y=h. Do as Stapel said and solve the perimeter equation for y in

terms of x, therefore, you will have h in the volume equation.

Now you can put the entire volume equation in terms of x, differnetiate, set to 0 and solve for x. There ya' go.

BTW, say hello to Radar for me.

I'm sorry, I couldn't help it.