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January 30th, 2007, 02:57 AM  #1 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  Right Circular Cone
Water is poured into a container in the shape of a right circular cone with radius 4 feet and a height of 16 feet. Express the volume V of the water in the cone as a function of the height h of the water. HINT GIVEN: The volume V of a cone of radius r and height h is V = (1/3)(pi)(r^2)(h). NOTE: Since the radius is 4 feet, does it mean the diameter of the cone is 8 feet? 
January 30th, 2007, 09:55 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,706 Thanks: 1356 
Yes, but you don't need that. The hint almost gives the answer; since the radius is a quarter of the height for the whole cone (and hence also for the water in the cone, assuming the cone is positioned with its axis vertical and vertex lowermost), just replace r with h/4 and state that h lies within the closed interval (0, 16) feet (since defining a function requires giving its domain). 
January 30th, 2007, 01:05 PM  #3 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  ok
Where did you get r = h/4?

January 30th, 2007, 02:58 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,706 Thanks: 1356 
The question gives the height and radius of the conical container, allowing their ratio to be calculated as 4:1. Since the ratio gives the "steepness" of the cone, it also applies to water at rest in the vertical cone.

February 2nd, 2007, 03:57 PM  #5 
Senior Member Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1  ok
Got it.


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