# Calculus

posted by
**chamy**
.

An open hemispherical bowl of radius R is slowly

draining through a small hole of radius r in the bottom

of the bowl. Let g be the acceleration due to gravity

and y be the depth of the water (which means the distance

from the water surface to the hole). Torricelliâ€™s

Law states that the speed of the droplets leaving the hole is

âˆš2gy . (This is actually the

speed that the droplets would acquire by falling from the water surface to the hole.)

(a) What is the meaning of the expression Ï€r2âˆš2gy ?

(b) In terms of y, what is the area of the water surface when the water is y cm deep?

(c) Assume that the bowl is initially full. How much time will be needed to drain it?