# Volume of Rotation

1. Aug 30, 2007

### danago

Find the volume of the solid generated by rotating the region trapped between the curve y3=x2, the y-axis, the line y=4 and the line x=0 around the y-axis.

I started by writing x as a function of y, explicitly:

$$x=y^{1.5}$$

Heres the graph i obtained, with the shaded area being the area to be rotated about the y axis.

$$V = \pi \int\limits_0^4 {(y^{1.5} )^2 dy = } \pi \int\limits_0^4 {y^3 dy = } 64\pi {\rm{ units}}^3$$

The answer in the book says it should be 631.65 units3. It looks to me as if they multiplied by $$\pi^2$$ instead of just $$\pi$$. Am i missing something, or am i on the right track?

Dan.

2. Aug 30, 2007

### Dick

It looks like 64*pi units to me as well. Are we both missing something?

3. Aug 30, 2007

### rocomath

i got the same answer and i haven't solved any volume problems in a long time

4. Aug 30, 2007

### Dick

That concludes it. The score is 3 against 1. The book answer is wrong. Not all that unusual.

5. Aug 31, 2007

### danago

Alright thats good to hear Thanks for confirming it guys

6. Aug 31, 2007

### P.O.L.A.R

Is it a solutions manual or the back of the book?

They did square pi but I dont see how they did. I wonder if they thought that pi should be squared because the radius (R(x)) is squared which is completely wrong. Quite strange really.