9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first oct...
1. Find parametric equations for each surface. a) The plane through the points (0, 0,0), b) The portion of the sphere x2 +y2 + c) The part of the cylinder y 16 (1,0,3), and (0, 2,3) 22-9 inside the first octant, that lies between the planes +4. 1. Find parametric equations for each surface. a) The plane through the points (0, 0,0), b) The portion of the sphere x2 +y2 + c) The part of the cylinder y 16 (1,0,3),...
(1 point) Find the volume of the solid that lies within the sphere x2 +y2 .2 16, above the xy plane, and outside the cone 2 (1 point) Find the volume of the solid that lies within the sphere x2 +y2 .2 16, above the xy plane, and outside the cone 2
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi 1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find...
(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
16. fs y2 dS, S is the part of the sphere x2 + y2 + z2 = 1 that lies above the cone z = Vx2 + y2 16. fs y2 dS, S is the part of the sphere x2 + y2 + z2 = 1 that lies above the cone z = Vx2 + y2
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2. 2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2. Hints: * Complete the square for ×2 + y2 + Z2-42+ (it is a sphere with center (0, 0,) Find the intersection to determine the region of integration 2. Find the area of the part of the surface of the sphere x2 + y2 + Z2-42 that lies within the paraboloid z-x2 + y2....
The region above the xy-plane that is inside both the sphere 2? + y2 + x2 = 4 and the cone 22 + y2 – 322 = 0, has density at a point given as f (x, y, z) = x2 + y2 What is the mass of the region?
(1 point) Find the surface area of the part of the sphere za + y2 + z = 81 that lies above the cone z= V22 + y2
(a) Let R be the solid in the first octant which is bounded above by the sphere 22 + y2+2 2 and bounded below by the cone z- r2+ y2. Sketch a diagram of intersection of the solid with the rz plane (that is, the plane y 0). / 10. (b) Set up three triple integrals for the volume of the solid in part (a): one each using rectangular, cylindrical and spherical coordinates. (c) Use one of the three integrals...