# Thread: Need help with computing the volume of a solid by revolving lines

1. ## Need help with computing the volume of a solid by revolving lines

How do you compute the volume of a solid formed by revolving the given region about the lines?

the directions are:

compute the volume of the solid formed by revolving the given region about the line

region bounded by y=2x, y=2 and x=0 about (a) the y-axis; (b) x=1

It has to be solved with a definite integral
V=∫A(x)dx,a,b

2. Originally Posted by db2dz
How do you compute the volume of a solid formed by revolving the given region about the lines?

the directions are:

compute the volume of the solid formed by revolving the given region about the line

region bounded by y=2x, y=2 and x=0 about (a) the y-axis; (b) x=1

It has to be solved with a definite integral
V=∫A(x)dx,a,b

A start for a) $\displaystyle \int \pi \frac{y}{2}^2dy=\frac{\pi}{4} \int y^2dy= \frac{\pi y^3}{12}$

A start for b) $\displaystyle \int \pi-\pi \frac{y}{2}^2 dy=\pi \int dy - \frac{\pi}{4} \int y^2dy=\pi y-\pi \frac{y^3}{12}$

Can you finish it off?

3. Thats what i needed thank you so much

4. Originally Posted by db2dz
Thats what i needed thank you so much
No problem, what did you get for the final results?

5. (a) 2(pi)/3

(b) 4(pi)/3

6. Originally Posted by db2dz
(a) 2(pi)/3

(b) 4(pi)/3

$\displaystyle a)\int^2_0 \pi \frac{y}{2}^2dy=\frac{2 \pi }{3}$

$\displaystyle b)\int^2_0 \pi-\pi \frac{y}{2}^2dy=2 \pi-\frac{2 \pi }{3}=\frac{4 \pi }{3}$