Determining the Volume of a Solid of Revolution

Key Questions

• How do you find the volume of the solid obtained by revolving the curve given by `x=3cos^3(t)`, `y=5sin^3(t)` about the `x`-axis?

  `y^2=25sin^6t=25(1-cos^2t)^3=25[1-(x/3)^{2/3}]^3`

  By Disk Method,

  `V=pi int_{-3}^3y^2 dx=25piint_{-3}^3[1-(x/3)^{2/3}]^3dx`

  Wataru · · Sep 20 2014

• How do you find the volume of the solid obtained by revolving the curve given by `x=3cos^3(t)`, `y=5sin^3(t)` about the `x`-axis?
• Question #fff79
• Find the volume of the solid obtained by rotating the region bounded by the curves `y=x^3` and `x`-axis in the interval `(1,2)`?