Posted by Danelle on Saturday, September 1, 2012 at 7:31pm.
Find the volume of the solid generated by revolving the region bounded by y= x^(1/2), y= 0, and x= 3 revolving around the yaxis.

math  Anu, Saturday, September 1, 2012 at 7:43pm
Draw graph of y= x^(1/2) to help you understand solution.
Rotation about yaxis means that the radius of the solid (length being swung around the axis is the xvalue).
it helps to solve for xvalue rather than try to substitute everything. x=y^2 where y>0
each disk or xvalue being swung around has an area of pi x^2 (area of a circle equals pi r^2) or in terms of y= pi (y^2)^2= pi Y^4
to make this a volume you need to multiply by the change in y (notation=dy)
so.....integrate
from the interval x=0 to x=3 you need to integrate...when x=0, y==0
when x=3, y= sqrt(3)
so integrate
/sqrt(3) pi(y^4) dy
0/
dont let y confuse youits just a variable like x. integrate normally

math  Damon, Saturday, September 1, 2012 at 7:48pm
y = x^.5
little cylinder shells of height y and thickness dx
V = int [ 2 pi x y dx } from x = 0 to x = 3
V = int [ 2 pi x^1.5 dx } from x = 0 to x = 3
V = (2 pi/2.5) x^2.5 at 3  at 0
V = (2 pi/2.5)( 3^2.5)

sorry, subtract from total  Damon, Saturday, September 1, 2012 at 7:52pm
I did under the curve.
V = pi (3)^2.5  (2 pi/2.5)( 3^2.5)
= 3^2.5 * pi [ 1  2/2.5 ]

math  pleh, Saturday, September 1, 2012 at 7:54pm
thanks

math  Damon, Saturday, September 1, 2012 at 7:54pm
By the way, you can do it either way.
Answer This Question
Related Questions
 MATH  Find the volumes of the solids generated by revolving the region in the ...
 Calculus  I would like to know if my answers are correct: Disclaimer: We are ...
 Calculus  Can you please check to see if these answers are correct? I have ...
 poly  the volume of the solid generated by revolving infinite region bounded by...
 calc  Find the volume of the solid generated by revolving the region bounded by...
 Calculus  5. Find the volume of the solid generated by revolving the region ...
 Math  Find the volume of the solid generated by revolving the region bounded by...
 math  1) A region is bounded by the line y = x and the parabola y = x2  6x + ...
 math  1) A region is bounded by the line y = x and the parabola y = x2  6x + ...
 Volume of a solid  calculus  Find the volume of the solid generated by ...
More Related Questions