Question

圆台的侧面积是什么?怎么推导的?

Answer 1

两个圆扇形面积之差.圆台的上下底半径 r,R,R的母线长为L1,r 的母线长为L2,

则圆台的母线长为L =L1- L2 ,L2/L1= r / R,

L2/(L1-L2) = r/(R-r) => (R-r) L2 = r (L1-L2) = r L

圆台的侧面积 S = π R L1-π r L2 = π [ R( L1-L2) + L2(R-r) ] = π ( R+ r) L