SOLUTION: 150 spherical marbles each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm. This vessel contains some water and the marbles are completely immersed. Find th

Algebra ->  Surface-area -> SOLUTION: 150 spherical marbles each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm. This vessel contains some water and the marbles are completely immersed. Find th      Log On


   

Question 847886: 150 spherical marbles each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm. This vessel contains some water and the marbles are completely immersed. Find the rise in the water level.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The rise in water is accomplished by displacing the water with the volume of the marbles.
Each marble has a volume of
V%5Bm%5D=%284%2F3%29%2Api%2AR%5E3=%284%2F3%29%2Api%2A%280.7%29%5E3=1.437cc
V%5Btot%5D=150%2AV%5Bm%5D=215.5 cc
The volume of a cylinder is V%5Bc%5D=pi%2AR%5E2%2AL
pi%2A%283.5%29%5E2%2AL=150%2A%284%2F3%29%2Api%2A%280.7%29%5E3
L=150%2A%284%2F3%29%2A%280.7%2F3.5%29%5E2%2A%280.7%29
L=150%284%2F3%29%281%2F25%29%287%2F10%29
L=56%2F10=28%2F5cm