>>218
K(a) = {(1+x^2)(1+y^2)(1+z^2)≦a}、R(a,t) = K(a) ∩ {z=t}
とおく。
Area of R(a,t)
= Area of {(1+x^2)(1+y^2) ≦ a/(1+t^2)}
= Area of {1+r^2 + (1/4)r^2sin 2θ ≦ a/(1+t^2)}
= (a/(1+t^2) - 1)/2∫[θ]1/(1+(1/4)sin2θ)dθ
= 2π(a/(1+t^2) - 1)/√5
∴ Vokume of V(a) = 2∫[0,√(a-1)] 2π(a/(1+t^2) - 1)/√5 dt = …
∴ V(125) - V(8) = …