# calculus help

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
x = 4(square root of (3y)), x = 0, y = 3;
about the y-axis

V=?????

1. 👍 0
2. 👎 0
3. 👁 64
1. x=4√(3y)
x^2 = 48y

To use discs, note that the radius of each disc is x, and the thickness is dy, so

v = ∫[0,3] πx^2 dy
= 48π∫[0,3] y dy
= 216π

To use shells, each shell has radius x, and height 3-y, so

v = ∫[0,12] 2πx(3-y) dx
= 2π∫[0,12] x(3-x^2/48) dx
= 216π

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### Calculus I don't understand

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2,

asked by Jackie on December 4, 2013
2. ### Calculus

a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y =

asked by Beth on November 3, 2011
3. ### calculus

Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the x-axis; 3) Find the volume of the

asked by Megan on June 9, 2011
4. ### CALCULUS MAJOR HELP!!!!!!

Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the

asked by Roni on December 4, 2013
5. ### Calculus volume stuff

Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the

asked by Roni on December 4, 2013
6. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips

asked by Tina on March 8, 2011
7. ### Calculus

This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume

asked by Jillian on April 5, 2008
8. ### calculus

Let A be the bounded region enclosed by the graphs of f(x) = x , g(x) = x3 . Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0.

asked by me on October 31, 2010
9. ### calculus edit

1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y is greater than or equal to 0 about the y-axis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about

asked by jimmy on May 4, 2007
10. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the line x = 4. x= 4y^2 , x = 4 Find the volume V of this solid.

asked by JESSICA on February 17, 2010
11. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 6 x^6 , y = 6 x , x >= 0 Find the volume V of this solid.

asked by bob on January 30, 2009

More Similar Questions