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?

1 Answer
Wataru
Sep 20, 2014

#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#

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