[PDF] and below the cone



Math 241 Quiz 12. 4/15/13. Name:

solid that lies within the cylinder x2 + y2 = 1 above the plane z = 0



Math 3202 Solutions Assignment #5 1. Find volume of the solid that

Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 4 above the xy-plane and below the cone z = ? x2 + y2. Solution: In sperical 



Solutions to Homework 9

Setup integrals in cylindrical coordinates which compute the volume of D. Solution: The intersection of the paraboloid and the cone is a circle. Since z = 2 ? 



??? ???

4. Set up the integral to find the volume of the solid bounded above by the hemisphere and below by the cone using cylindrical coordinates z = 4 ? x2 ? y2.





Contiune on 16.7 Triple Integrals Figure 1: ???Ef(x y

https://www3.nd.edu/~zxu2/triple_int16_7.pdf



Multivariate Calculus . . . . . . . . . . . . . Polar Double Integral Problems

Find the volume of the solid under the cone z = ?x2 + y2 and above the ring 4 ? x2+y2 ? 25. Comment: The domain D is the nearly the same as in the last 



Math 241 Quiz 10. 4/4/12. Name:

§15.4 #25 (7 points): Use polar coordinates to set up a double integral expressing the volume of the solid which lies above the cone z =?x2 + y2 and below 



Solutions to Midterm 1

Evaluate ???E z dV where E is the solid that lies above the paraboloid z = x2 + y2 and below the half cone z = ?x2 + y2. Solution: x = r cos?



= ?? = ??

4. Set up the integral to find the volume of the solid bounded above by the hemisphere z = 4 ? x2 ? y2 and below by the cone z = 3x2 + 3y2 

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