圆台(棱台）的体积公式证明圆台（棱台）
圆台（棱台）是由圆锥（棱锥）截成的
为打字方便，设上下底面积S1，S2，上下两个棱（圆）锥高h1,h2,
h2-h1=h, 由相似知√S1/√S2=h1/h2
不妨设h1=k√S1,则h2=k√S2, h=h2-h1=k(√S2-√S1)
k=h/(√S2-√S1)=h/[S2^(1/2)-S1^(1/2)]
棱(圆)锥体积=(1/3)[S2h2-S1h1]=(1/3)[S2k√S2-S1k√S1]
=(1/3)k[S2^(3/2)-S2^(3/2)]
=(1/3)[h/(√S2-√S1)]*[S2^(3/2)-S2^(3/2)]
=(1/3)h[S2^(3/2)-S2^(3/2)]/[...全部
圆台（棱台）是由圆锥（棱锥）截成的
为打字方便，设上下底面积S1，S2，上下两个棱（圆）锥高h1,h2,
h2-h1=h, 由相似知√S1/√S2=h1/h2
不妨设h1=k√S1,则h2=k√S2, h=h2-h1=k(√S2-√S1)
k=h/(√S2-√S1)=h/[S2^(1/2)-S1^(1/2)]
棱(圆)锥体积=(1/3)[S2h2-S1h1]=(1/3)[S2k√S2-S1k√S1]
=(1/3)k[S2^(3/2)-S2^(3/2)]
=(1/3)[h/(√S2-√S1)]*[S2^(3/2)-S2^(3/2)]
=(1/3)h[S2^(3/2)-S2^(3/2)]/[S2^(1/2)-S1^(1/2)]
=(1/3)h[S2+(S2S1)^(1/2)+S1]
=(1/3)h(S1+√S1S2+S2)。
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