Question

有一个大扇形,里面有一个小扇形和大扇形是同心圆.已知大扇形弧长为L1,小扇形弧长为L2,

Answer 1

设圆心角为θ,大小扇形半径分别为R和r,则R-r=d

L1=(θ/360)*2πR,L2=(θ/360)*2πr

(θ/360)πR=L1/2,(θ/360)πr=L2/2

大扇形面积减小扇形面积

=(θ/360)πR²-(θ/360)πr²

=(θ/360)π(R²-r²)

=(θ/360)π(R+r)(R-r)

=[(θ/360)πR+(θ/360)πr]*d

=(L1/2+L2/2)d

=(L1+L2)d/2