Find the volume of the solid generated by revolving the region bounded by y=sqrt(x), y=0, and x=3 about the y-axis.

My take on this was:
x=y^2 on [0,9] since the information states that in terms of x, the interval is [0,3]. Therefore, by plugging in, (0)^2=0 and (3)^2=9.

So:
int (0,9) ((pi)(y^2)^2) dy
=(pi)(1/5(x^5))|(0,9)
Volume=(59049(pi)/5) cu. units.

Correct?

Question

Find the volume of the solid generated by revolving the region bounded by y=sqrt(x), y=0, and x=3 about the y-axis.

My take on this was:
x=y^2 on [0,9] since the information states that in terms of x, the interval is [0,3]. Therefore, by plugging in, (0)^2=0 and (3)^2=9.

So:
int (0,9) ((pi)(y^2)^2) dy
=(pi)(1/5(x^5))|(0,9)
Volume=(59049(pi)/5) cu. units.

Correct?

anonymous · Answer

The main problem I have is that I feel as though I should be subtracting the volume of the area between y=0 and x=y^2 in order to get an accurate measurement. Am I right? How do I do this?