x=yx = \sqrt{y}x=y 高さを hhh とすると V=π∫0h(y)2 dy=π[12y2]0h=πh22V = \pi\int_0^h (\sqrt{y})^2\,dy = \pi\left[\frac{1}{2}y^2\right]_0^h = \frac{\pi h^2}{2}V=π∫0h(y)2dy=π[21y2]0h=2πh2 dVdt=8\frac{dV}{dt} = 8dtdV=8 より V=πh22=8th=16tπV = \frac{\pi h^2}{2} = 8t \qquad h = \sqrt{\frac{16t}{\pi}}V=2πh2=8th=π16t h′=1216πt=2πt cm/sech' = \frac{1}{2}\sqrt{\frac{16}{\pi t}} = \frac{2}{\sqrt{\pi t}} \text{ cm/sec}h′=21πt16=πt2 cm/sec