A student was asked to find the volume of the bowl-shaped figure generated when the curve y = x2 from x = 0 to x = 2 is revolved around the y-axis. She used the disk method and found the volume to be . To check her work she used the method of cylindrical shells and found the same answer: .
The second part of the questioned asked for the value of x for which the bowl would be half full. So she first solved the equation and found . This is a y-value so the corresponding x-value is . She again checked her work by shells by solving and found that . (This is the x-value.)
Both computations are correct. Can you explain to her why her answers are different? Use the comment box below to share your explanations. I will post mine in a week or so.