SOLUTION: The height of the cone is 16cm and the radius is 12cm, and the question is that the cone is exactly half full of water by volume. How deep is the water in the cone

Algebra ->  Volume -> SOLUTION: The height of the cone is 16cm and the radius is 12cm, and the question is that the cone is exactly half full of water by volume. How deep is the water in the cone      Log On


   

Question 912147: The height of the cone is 16cm and the radius is 12cm, and the question is that the cone is exactly half full of water by volume. How deep is the water in the cone
Found 2 solutions by josgarithmetic, ewatrrr:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
volume of cone, %281%2F3%2916%2Api%2A12%5E2
Half full, %281%2F2%29%281%2F3%29h%2Api%2A12%5E2=%281%2F3%2916%2Api%2A12%5E2
Simplify and find h.

Note that the cone was HALF-FILLED, so assuming axis of the cone is up-down, the base may be either up or down.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

 

full = %281%2F3%29pi%2812%5E2%2916+= 768

half-full = 384pi

Note: h = (16/12)r in general

half-full = %281%2F3%29pi%28r%5E2%29%284%2F3%29r+= 384pi

(4/9)r^3 = 384

r^3 = 864

r = root%283%2C864%29

h = (4/3)root%283%2C864%29, depth of the water when half-full