Question

一圆柱形容器的内径位3厘米,内壁高30厘米,容器内成有10厘米高的水.

Answer 1

R=3 cm,r=2 cm

①当 h0=10 cm

πR²h0 + πr²h = πR²h

h = R²/(R²-r²) * h0 = (9/5)*10 = 18 cm

②当 h0=20 cm时,

h = R²/(R²-r²) * h0 = 36 cm> 30 cm,

这说明此时水会溢出容器,所以

h=30 cm,此时有πr²h-πR²(h-h0) = 3π cm³的水溢出