设圆柱形容器底面半径为R,高为H,
2πR²+2πRH=s
H=(s-2πR²)/(2πR)
圆柱形容器的容积=V
V=πR²H
=πR²(s-2πR²)/(2πR)
=0.5R(s-2πR²)
=0.5sR-πR³
V'=0.5s-3πR²
另V'=0,0.5s-3πR²=0,R²=0.5s/(3π),R=√[0.5s/(3π)],
H=(s-2πR²)/(2πR)=√[(2s)/(3π)].
设圆柱形容器底面半径为R,高为H,
2πR²+2πRH=s
H=(s-2πR²)/(2πR)
圆柱形容器的容积=V
V=πR²H
=πR²(s-2πR²)/(2πR)
=0.5R(s-2πR²)
=0.5sR-πR³
V'=0.5s-3πR²
另V'=0,0.5s-3πR²=0,R²=0.5s/(3π),R=√[0.5s/(3π)],
H=(s-2πR²)/(2πR)=√[(2s)/(3π)].