($15.5) Find the area of the part of the plane 2 x 3 ytz 6 that lies inside the cylinderx2+y2 4 Answer: the area=4...
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.
Find the area of the part of the plane 2r +5yz10 that lies inside the cylinder 2 29
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 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...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1, above the xy-plane, and below the plane z = 1 + x. Let S be the surface that encloses E. Note that S consists of three sides: S1 is given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2 + y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
6. Let S be the part of the cylinder x2 + y2 = 4 that lies between the two planes z = 2 – X and z = –2 – x. Note that S meets either plane on an ellipse, equipped with the outward normal of the cylinder. Sketch S and find the flux of the vector field F = (2x, y, x) through S.
Solve c and d Please. Find the area of the following surfaces. a) The part of the plane 3z + 2y +z 6 that lies in the first octant. b) The part of the cone zVy that lies between the plane y z and the cylinder y-x c) The surface with vector equation r(u, u) = (u . cos(v), u . sin(v), u) , where 0 u 1, 0 v S T. d) The portion of the unit sphere that...
Find the area (surface area) of the part of the hyperbolic paraboloid z = y2 - x that lies between the cylinders x + y2 = 1 and x² + y2 = 4
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....
Compute the following surface areas: (a) the surface area of that part of the plane z = Ar + By C which lies inside the y2 elliptical cylinder 1. (b) the surface area of that part of the cylinder r2 +y2 the sphere 2 y 2 0 which lies inside 2ar 4a2. (Notice the symmetry)