SOLUTION: The volume of the water in a hemisphere having a radius of 2 m is 2.05 cu. m. Find the height of the water. It says in our book that the height should be 0.602 m. I have already

Algebra ->  Volume -> SOLUTION: The volume of the water in a hemisphere having a radius of 2 m is 2.05 cu. m. Find the height of the water. It says in our book that the height should be 0.602 m. I have already       Log On


   

Question 1168325: The volume of the water in a hemisphere having a radius of 2 m is 2.05 cu. m. Find the height of the water. It says in our book that the height should be 0.602 m.
I have already tried solving it but I got lost in the middle. I hope you can help me with this. Thank you!

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The volume of the water in a hemisphere ( the water in the hemispherical bowl) is given by
V+=+%28pi%2F3%29h%5E2%2A%283r-h%29, where r is the radius and h+is height.
Given that the radius of the hemisphere is r=2m and the volume of water is V=2.05m%5E3, we have:

2.05+=+%28pi%2F3%29h%5E2%2A%283%2A2-h%29
2.05+=+%28pi%2F3%29h%5E2%2A%286-h%29
1.9576058000303127=+6h%5E2-h%5E3
6h%5E2-h%5E3-1.9576058000303127=0.......factor
-1+%28h+-+5.9446%29+%28h+-+0.60222%29+%28h+%2B+0.546824%29+=+0
-1+%28h+-+5.9446%29=0=>h=5.9446.....disregard because is greater than diameter of the sphere
%28h+%2B+0.546824%29+=+0=> h=-+0.546824.....disregard negative solution
%28h+-+0.60222%29=0=>h=0.60222
answer:
=> h≈0.602