就 一网友所问 法1. 极限法 微积分形式
V棱台
=
V圆台
=
∫(0，h)π((r2-r1)H/h+r1)²dH
=
π/h²∫(0，h)
((r2-r1)²H²+2hr1(r2-r1)H+r1²h²)dH
=
π/h²
((r2-r1)²/3H³+hr1(r2-r1)H²+r1²h²H)
Ⅰ(0，h)
=
πh((r2-r1)²/3+r1(r2-r1)+r1²)
=
πh((r2-r1)²+3r1(r2-r1)+3r1²)/3
=
πh(r2²+r1r2+r1²)/3
=
h(S1+√(S1S2)+S2)/3
得证
ps.
上述
微积分法
极限形式
详见
