问题描述：
已知一个圆锥的高为6cm,母线长为10cm,求圆锥的内切球的体积,和外接球的表面积要过程
问题解答：
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设圆锥高h,母线长l,底面半径a,内切球半径r,外接球半径R,则有
h = 6, l = 10
a = sqrt(l^2-h^2) = 8
从图中可见到 x^2+r^2 = y^2
而x值显然为 x = 10-8 = 2, y = h-r = 6-r
因此 2^2+r^2 = (6-r)^2
=>12r = 32
=>r = 8/3
V内= 4/3*pi*r^3 = 4/3*8^3/3^3*pi = 2048/81*pi
对于外接球
显然有 R^2 - 8^2 = (R-h)^2
=> R^2 - 64 = (R-6)^2
=>12R = 100
=>R = 25/3
S外= 4*pi*R^2 = 4*pi*25^2/3^2 = 2500/9*pi
h = 6, l = 10
a = sqrt(l^2-h^2) = 8
从图中可见到 x^2+r^2 = y^2
而x值显然为 x = 10-8 = 2, y = h-r = 6-r
因此 2^2+r^2 = (6-r)^2
=>12r = 32
=>r = 8/3
V内= 4/3*pi*r^3 = 4/3*8^3/3^3*pi = 2048/81*pi
对于外接球
显然有 R^2 - 8^2 = (R-h)^2
=> R^2 - 64 = (R-6)^2
=>12R = 100
=>R = 25/3
S外= 4*pi*R^2 = 4*pi*25^2/3^2 = 2500/9*pi
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