r=a(1+cosθ)
x=a(1+cosθ)cosθ
dx/dθ=-asinθ(1+2cosθ)
dx/dθ=0となるのはθ=0,(2/3)π,π{0≦θ≦π}

V=π∫[θ=(2/3)π〜0]f(x(θ))^2(dx/dθ)dθ
-π∫[θ=(2/3)π〜π]g(x(θ))^2(dx/dθ)dθ
=π∫[θ=0〜π](a(1+cosθ)sinθ)^2(asinθ(1+2cosθ))dθ
=(a^3)π∫[t=-1〜1](1+4c+4c^2-2c^3-5c^4-2c^5)dt
=(a^3)π[t+(4/3)t^3-t^5][t=-1〜1]
=(8π/3)(a^3)