SOLUTION: A cone is filled with water up to the halfway mark. Is the volume of water three quarters the volume of the cone? Find the ratio of the volume of the water in the cone : The vo

Algebra ->  Volume -> SOLUTION: A cone is filled with water up to the halfway mark. Is the volume of water three quarters the volume of the cone? Find the ratio of the volume of the water in the cone : The vo      Log On


   

Question 978461: A cone is filled with water up to the halfway mark. Is the volume of water three quarters the volume of the cone?
Find the ratio of the volume of the water in the cone : The volume of the cone
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Point up or down, not stated. Try cutting the volume into two parts.

V=h%2Api%2Ar%5E2, whole cone.
k is some constant so that h%2Fr=k.
r%2Fh=1%2Fk
r=h%2Fk

Part with the point, %28h%2F2%29pi%2A%28h%2F%282k%29%29%5E2, from vertex point to the halfway mark.%28h%5E2%2Api%29%2F%282%2A2%2A2%2Ak%5E2%29
highlight_green%28%28h%5E2%2Api%29%2F%288k%5E2%29%29

Part with the original main base, h%2Api%2Ar%5E2-%28h%5E2%2Api%29%2F%288k%5E2%29
h%2Api%2A%28h%2Fk%29%5E2-%28h%5E2%2Api%29%2F%288k%5E2%29
highlight_green%28%28h%5E2%2Api%29%2F%28k%5E2%29-%28h%5E2%2Api%29%2F%288k%5E2%29%29

I have not finished. You can now try to compare each of these parts to the original cone's volume.