marbles of diameter 1.4cm is dropped into a cylindrical beaker of diameter 7cm,containingsome water.how many marbles should be dropped into the beaker,so that the water level rises by 5.6cm?
Marbles have a density greater than that of water so all of them will sink. Each marble will displace an amount of water equal to it volume. I will assume there is enough water already in the cylinder such that each marble will be completely submerged.
The volume of each marble is:
v = (4/3)(pi)(d/2)^3 = [(pi)d^3]/6.
The volume we want to add to the water in the beaker (which is a cylinder) has a diameter of 7 cm and a height of 5.6 cm, or:
V = (pi)(7 cm)^2 * (5.6 cm) = n*v where n is the number of marbles.
So calculate the volume of each marble from the above formula and
n = V/v.
-Dan