Question

A hemispherical tank of diameter, 10m, is filled by water issuing from a pipe of radius 20cm at 2m per second. Calculate, correct to three significant figures, the time, in minutes it takes to fill the tank.

Answer 1

volume = (4/3) pi r^3
r = 5 meters
so
volume = (4/3) pi * 125 m^3
rate through hose = pi r^2 * 2 m^3/s = pi .2*.2 * 2 = .08 pi m^3/s
so
t in seconds = 167 pi / .08 pi
in minutes 167 / (.08 *60) = 34.7 min (boring ! )

Answer 2

hemisphere, so 1/2 the volume

Answer 3

Volume of hemisphereical tank= (2/3)(pi)(5m)^3
Volume of water issuing out= is of a cylinder shape so= (height/s)(pi)(radius)^2
Which is (2m/s)(pi)(0.2m)^2.
Note i changed all quantities into meters. 100cm=1m
Compute all this and change it to minutes the answer and you will get 17.366mins Voila!!