SOLUTION: A heavy metal sphere with radius 10cm is dropped into a right circular cylinder with base radius of 10cm. If the original cylinder has water in it that is 20cm high, how high is th

Algebra ->  Volume -> SOLUTION: A heavy metal sphere with radius 10cm is dropped into a right circular cylinder with base radius of 10cm. If the original cylinder has water in it that is 20cm high, how high is th      Log On


   

Question 173463: A heavy metal sphere with radius 10cm is dropped into a right circular cylinder with base radius of 10cm. If the original cylinder has water in it that is 20cm high, how high is the water after the sphere is placed in it?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the cylinder with water level at 20 cm is V=%28pi%29%2810%29%5E2%2820%29
:
2000%28pi%29cu cm
:
volume of the sphere is V=%284%2F3%29%28pi%29%2810%29%5E2
:
133.33%28pi%29
:
the water level has to rise to account for the displaced volume water when the sphere is placed in it and has to be equal to the volume of the sphere.
:
so we will add the volume of the sphere to the volume of the cylinder and solve for the unknown h.
:
2000%28pi%29%2B133.33%28pi%29=2133.33%28pi%29
:
2133.33%28pi%29=%28pi%29%2810%29%5E2h
:
2133.33=100h
:
highlight%28h=21.33%29cm is the level of the water after the sphere is place in it.