Thursday

July 31, 2014

July 31, 2014

Posted by **K** on Tuesday, January 29, 2013 at 12:14am.

- calculus -
**Steve**, Tuesday, January 29, 2013 at 10:59amSince the radius of the surface of the water is r^2 = x^2+y^2, it looks to me like the volumes are

paraboloid: v = ∫[0,4]πz dz = 8π

cone: v = ∫[0,4]πz^2 dz = 64/3 π

hyperboloid: v = ∫[1,5]π(z^2-1) dz = 112/3 π

Hmm. Not what I expected, the cone having greater volume than a round-bottomed paraboloid. However, it makes sense when you see that the cone's radius at the top of the water is √8, while the paraboloid's is only 2.

**Related Questions**

AP calculus - The base of a cone-shaped tank is a circle of radius 5 feet, and ...

Calculus - A container in the form of a right circular cone of height 16 cm and ...

Calculus 2 - A cone is filled w/ freshwater (w=62.4 lb/ft^3). Determine the ...

calculus - A hollow cone has height 5 feet and base diameter 4 feet. The vertex...

Calculus II - A cone-shaped water reservoir is 20 ft. in diameter and 20 ft. ...

calculus - Let C be the curve which is the intersection of the half-cone S1 = {(...

Statistics - Five friends go bowling and finish with the following scores. Jim ...

math - The volume of a cone is three hundred cubic kilometers. If the radius of ...

math - The volume of a cone is three hundred cubic kilometers. If the radius of ...

math - Resolved QuestionShow me another » AP Calculus related rates problem? The...