一個圓臺的母線長L等于上、下底面半徑R1,R和的一半,將圓臺補充為完整的圓錐,上底面以上部分的圓錐母線長L1,整個圓錐的母線長=L1+L:
(1/2)(L+L1)(2Rπ)-(1/2)L1(2R1π)=32π,即:
(L+L1)R-L1R1=32,
LR+L1R-L1R1=32...(1)
又L=(1/2)(R+R1),
2L=(R+R1),...(2)
縱向截面2個三角形相似:
R1:R=L1:(L1+L),
即(L1+L)R1-L1R=0,
L1R1+LR1-L1R=0...(3)
解方程組(1),(2),(3),
(1)+(3):
(LR+L1R-L1R1)+(L1R1+LR1-L1R)=32+0,
LR+LR1=32,
L(R+R1)=32,
將(2),2L=(R+R1),即(R+R1)=2L代入上式:
L(2L)=32,
L²=16,
L=4