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)#?