Find the volume of the portion of the sphere, /2 and z = 0 using (i) cylindrical coordinates that is contained between...
1. Use cylindrical coordinates to SET UP the integral for the volume of the portion of the unit ball, 22 +232 + x2 < 1, above the plane z = 12 2. (a) Write in spherical coordinates the equations of the following surfaces: (i) x2 + y2 + x2 = 4 (ii) z = 3x2 + 3y2 (b) SET UP the integral in spherical coordinates for the volume of the solid inside the surface 22 + y2 + x2 =...
Using an integral in spherical coordinates, find the volume of a sphere of radius 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.)
Find a parametrization of the surface. The portion of the sphere x² + y2 + z = 2 between the planes z = and z= - 2 2 What is the correct parameterization? Select the correct choice below and fill in the answer boxes within your choice. (Type exact answers.) O A. r(0,0) = i+ k, sos sos sps sos OB. r(0,0) = O C. rq,0) = sos sos OD. r(0,0) =i+j+ k sos 1.ses
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
3. [4 marks] Using cylindrical polar coordinates, or otherwise, find the value of the surface integral 1 = []6.2? ds, where S is the part of the cone z = z? + y that lies between the planes z = 2 and 2=5.
Cale3 Final Take Home (19S) NAME ID Dac Monday (May 6> (Show sact valuc and Show all your work by using both Cyl coordinates for hoth part I and part 2) Cylindrical & Spherical 1. Find the volume of the solid E between +y') fa cone and-xta semi-sphere) by evaluanting the triple insegral V-ldrby any coondinates 2. will he the denominuo i 2 Fins the centroithEbre, Illis an the -axi) he er f formula for the centroid)y
Cale3 Final Take...
Set up only
b. Find the volume of the solid bounded by z x2 y2 and z 3 in spherical coordinates. Set-up only (OJ 7a. Change to spherical coordinates. Set-up only.X 2. f(x, y,z)dzdxdy b. Find fffe'd/where E is the region bounded by z (x2 + y2)2 and z 1, inside x2 + y2 4 in cylindrical coordinates. Set-up only
b. Find the volume of the solid bounded by z x2 y2 and z 3 in spherical coordinates. Set-up only...
find the (3) use cylindrical Coordinates to Volume of the Solid bounded by Z=9-2²-9² and z=5. (3)