Using an integral in spherical coordinates, find the volume of a sphere of radius 2.
Using an integral in spherical coordinates, find the volume of a sphere of radius 2.
Using an integral in cylindrical coordinates, find the volume of a cylinder of radius 1 and height 2.
6. Set up a triple integral using cylindrical or spherical coordinates to find the volume of the solid that lies between the surfaces 2 - 27- 2x - 2y' and 2=x-v Evaluate one of your triple integrals to find the exact volume of this solid.
Use spherical coordinates to find the volume of the region bounded by the sphere p= 34 cos p and the hemisphere p = 17 z 20. The volume of the region bounded by the sphere and the hemisphere is (Type an exact answer using a as needed.)
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the spheres r2+94:2-4 and r2+92+ะ2-16 and above the cone V+v) or Recommend separating! 5. Using spherical coordinates, find the volume of the solid that lies within the sphere r2+y2+2 9, above the ry-plane, and below the cone ะ-V/r2 + y2 Reconnnend separating! 6. Using spherical coordinates, evaluate the triple integral: 2 + dV where E is the portion of the solid ball 2+2+2 s 4 that...
Find the volume of the portion of the sphere, /2 and z = 0 using (i) cylindrical coordinates that is contained between the planes z and () spherical coordinates.
11. Using spherical coordinates, find the volume of the region above the cone o = and below the sphere p= 2.
ser up the triple integral in spherical coordinates to express the volume inside of a cone phi = pi/6 , and inside a sphere p=5
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts) Use...
Use spherical coordinates to find the volume of the region outside the cone p=1/4 and inside the sphere p = 6 cos Q. 6 The volume is . (Type an exact answer, using a as needed.) Use spherical coordinates to find the volume of the region outside the cone /4 and inside the sphere pocos The volume is Type an exact answer, using as needed.)
Find the volume of the solid Use spherical coordinates to find the mass of the solid bounded below by the cone z=« .) and above by the sphere x+y+ =9if its density is given by 8(x,y,2) = x+ y+Z. JC Use spherical coordinates to find the mass of the solid bounded below by the cone z=« .) and above by the sphere x+y+ =9if its density is given by 8(x,y,2) = x+ y+Z. JC