Showing posts with label calculus. Show all posts
Showing posts with label calculus. Show all posts

Thursday, May 14, 2009

Using Shell or Disc Method to Find Volume of the Solid

Disc method and Shell(cylinder) method of integration are the two different methods of finding volume of solid of a revolution, using rectangular coordination system the functions are defined in terms of x in the below problem.

Topic : Disc or Cylinder Method of Finding Volume of the Sphere.

Problem : Use the disc or shell method to find the volume of the solid generated by revolving the regions bounded by the graphs of the equations about the x axis. y=x3 y=0, x=2

Solution :

y = x3 => 3√y = x
or (y)1/3 = x
or x = y1/3

Volume of a Solid by rotating about x-axis is given by:

V = 2πabp(y)h(y) dy
here p(y)=y1/3, h(y)=y
when x = 2 and y = 33 = 8
So a = 0 and b = 8
Plugging in all the values in the formula, we get

V = 2π08(y)1/3.y dy

= 2π08(y)4/3 dy (as 1/3 + 1/1 = (1+3)/3 = 4/3)

= 2π[y7/3/(7/3)0]8 (as 4/3 + 1/1 = (4+3)/3 = 7/3)

= 2π[(8)7/3/(7/3)- (0)7/3/(7/3)]

= 2π[((2)3)7/3/(7/3)]

= 2π(27/(7/3))

= 2π(128/(7/3))

= 2 * 3 * 128 * π / 7

= 768π /7


So this how the volume of Solid of revolution is determined when the equations about the x axis.
For more help write to our calculus help.