# Help with work problem

• June 3rd 2008, 11:18 PM
khuezy
Help with work problem
The region R bounded by the y-axis, the lines y=4 and y=0, and the portion of the
ellipse

(x^2) +4(y-4)^2=100

between the points (6,0) and (10,4) is revolved around the y-axis to form
a container that is full of water. (See picture below.)

____________
...................'
................../
................./
...............-

How do I set this up? Using the disk method?

Thanks.
• June 4th 2008, 12:18 PM
ebaines
Yes - you each disc is centered on the y-axis, and you have the radius of each disc: R^2 = 100- 4(y-4)^2. The incremental volume of each disc is therefore:

$

dV = \pi (100-4(y-4)^2) dy
$

Integrate this from y = 0 to y =4.