10) Suppose you have a homework question asking you to find the volume of the solid that lies above the cone z-Vx2...
3. Find the volume of the solid in the first octant that lies above the cone z = 3(x + y) and inside the sphere x2 + y2 + z2 = 42. Use spherical coordinates.
3. Find the volume of the solid in the first octant that lies above the cone z = 13(x+ + y) and inside the sphere x2 + y2 + y2 = 42. Use spherical coordinates. 4. Determine if the vectorfield F(x, y) - (x + y)i + (2xy + y) is conservative If it is, find a potential function
Use spherical coordinates to find the volume of the solid that lies above the cone z = 3x2 + 3y2 and below the sphere x2 + y2 + z? first octant. Write = 1 in the v=L"!" " * sinħapapao 1. 0 2. 1 d = 3. À b = 4. 7T 2 f= 5. 6 a = < 6. Í C = 7. 21 ve Ja Ja Ja p sin qapaqau 1. 0 2. 1 d = 3. b=...
Question 4 (3.6 points) Use spherical coordinates to find the volume of the solid that lies below the cone z = Vx2 + y2 and above the sphere x2 + y2 +22 = 1. Write V= =("sin ødpdøde 1. 0 2. 1 d= > 3. e= > 4. 2 II < 5. < a= 6. Í < C= 7. 2a b= < 8. 9. 34
(1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2 (1 point Find the volume of the solid that lies within the sphere x2 + 2 + z-64 above the xy plane, and outside the cone z 8V x2 y2
5. The solid E lies above the cone z = 3V x2 + y2, inside the cylinder x2 + y2 = 4 and below the plane z = 8; see Fig.2. (a) Write the equations of those three surfaces in cylindrical coordinates and say in which horizontal plane the cone intersects the cylinder. (b) Set up a triple iterated integral in cylindrical coordinates, for this triple integral SSI r’dV
Use spherical coordinates. 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)
5a. The solid E lies above the cone z =V3V2 + y and below the sphere cº + y2 + 2 = 9. Completely set up, but DO NOT EVALUATE, the triple integral Ssse (y+z)dV in spherical coordinates. Show appropriate work for obtaining the limits of integration and include a sketch. Your answer should be completely ready to evaluate. (9 points) 5b. Completely set up, but DO NOT EVALUATE, the same triple integral ple (y + x)2V from part (a),...
please help with Q1 and 3 1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
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...