Thread: surface areas and volumes

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?

Originally Posted by anjana

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