Wednesday

April 23, 2014

April 23, 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**

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

Calculus - Fuel is flowing into a storage tank which can be filled to a depth of...

Calculus - Fuel is flowing into a storage tank which can be filled to a depth of...

calculus - 1. A conical reservoir has a depth of 24 feet and a circular top of ...

physics - This is my lab project and i need help in how to start to solve this ...

Math - At a pet store, Rhonda paid $11.50 for 3 dog bowls and 4 bones. Kelly ...

Math - a bathtub can be filled by the hot and cold water pipes in four minutes ...

math - a bathtub can be filled by the hot and cold water pipes in four minutes ...

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

Physics - A water tower is filled with fresh water to a depth of 6.38 m. What is...