# Calculus

posted by Anonymous

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 0.5x^2, y = 2, and x = 0 about the line y = 2.

A. 8pi/15
B. 32pi/15
C. 64pi/15
D. 4pi/15
E. 16pi/15

1. Steve

v = ∫ πr^2 dx
where r=2-y
v = ∫[0,2] π(2-x^2/2)^2 dx

or

v = ∫ 2πrh dy
where r=2-y and h=x
v = ∫[0,2] 2π(2-y)√(2y) dy

2. Anonymous

How do you know the r is 2-y and not just y?

3. Reiny

Because it is rotated about the line y = 2 ,
not y = 0 , which would have been the x-axis

## Similar Questions

1. ### Calculus

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=ln x, y=0, x=1, x=3 Please show the steps in your work, thanks! :)
2. ### Calculus

"Find the volume of the solid generated by revolving the region bounded by the graphs of the given equations about the indicated lines: y = 2x^2 y = 0 x = 2 About the line y = 8"
3. ### calculus

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = 6 − x y = 0 y = 5 x = 0
4. ### calculus

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 the x-axis,the y-axis,and the line x = 4
5. ### calculus

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 a)the line x = 4
6. ### calculus

find the volume of the solid generated by revolving the region bounded by the graphs of the equations y=2sqrtx, y=o, x=3 about the x-axis.
7. ### Calculus

Find the volume or the solid generated by revolving around the region bounded by the graphs of the equations about line x=6. xy=6, y=2, y=6, and x=6
8. ### Calculus Voulme

find the volume of the solid generated by revolving the region r bounded by the graphs of the given equations about the y-axis. x^2+y^2=1 x=1 y=1
9. ### Math (Calculus)

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. (Use Disc Method) y=3(2-x), y=0, x=0
10. ### Math (Calculus)

Use the disc method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y=x^3, y=0, x=2 a)the x-axis b)the line x=4

More Similar Questions