## blackstreet23 one year ago Let Vx and Vy represent the volumes of the solids that result when the region enclosed by y=3x, y=0, x=1, x=b (b>1) is revolved about the x and y axis, respectively. Is there a value of b such that Vx=Vy?

1. anonymous

Region of interest:|dw:1433735228846:dw|

2. anonymous

The solid we get upon revolving about the $$y$$ axis: |dw:1433735322750:dw| and the solid we get upon revolving about the $$x$$ axis: |dw:1433735432439:dw|

3. anonymous

The volumes of each are given by the integrals $V_y=2\pi\int_1^bx\times3x\,dx=6\pi\int_1^bx^2\,dx$and$V_x=\pi\int_1^b(3x)^2\,dx=9\pi\int_1^b x^2\,dx$Assuming $$b$$ is fixed, what do you think? Hint: Try writing $$V_x$$ in terms of $$V_y$$, or the other way around.

4. blackstreet23

Thanks a lot pal for your help!!!