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 specified line x = 4.
y=x³ y=0, x=2

Solution :
y = x³
Here the solid is rotating along y axis.
So a = 0, b = 4 (as x varies from 0 to 4)
So Volume of a Solid by rotating about y-axis is given by:

V = 2π₀∫⁴ x³ . x dx

= 2π₀∫⁴ x⁴ dx

= 2π[x⁵/5 ₀]⁴

= 2π[(4)⁵/5 - (0)⁵/5]

= 2π[1024/5]

= 2048π/5

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.