   SEARCH HOME Math Central Quandaries & Queries  find the volume of the solid formed when region bounded by y=x/3, y=2 and the y-axis. it is revolved about the x-axis. the assignment was to use both the washer method and the shell method but when i solved for the volume, i got different answers. i think my shell method is wrong because i know i'm having difficulties with using "dy" instead of "dx" here's my work so far: washer method: R = 2, r = x/3 V=pi*integral from 0 to 6*4-(x2/9)dx it becomes 16pi because after the integral it is pi (4x-(x3/27)) and then i evaluated it SHELL METHOD: R = y, H = x = 3y V = 2pi*integral from 0 to 6*3y2dy it becomes 2pi(y3), evaluating it at 6 which turns out to be 432pi but there's a huge difference between my two answers.. could you please help me find my mistake? thanks, christina Hi Christina,

I agree with your washer method but there is one error in your shell method. In the shell method integral you are integrating with respect to y so the limits on the integral must be from y = 0 to y = 2. It looks like you have the limits as
x = 0 to x = 6.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.