Question

Find the volume of the solid formed by revolving the curve, r=a(1+cosθ), about the initial line.

Answer 1

$V=\int\frac{2}{3} \pi*r^2 sin A$ da

$a=\theta$

$\frac{2\pi}{3}∫a^3*(1-cos a)^3 sinA$ da

$t=1-cos A$

Sin A $da=dt$

$a=t=0,$

$a=\pi,$

$t=2$

$Volume=\frac{8}{3} *\pi*a^3$