13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S. 13. (1 point) Let S be the part of the paraboloid 1 222y that lies above...
Let S be part of the paraboloid \(z=x^{2}+y^{2}\) that lies under the plane \(z=4\). Evaluate the surface integral \(\iint_{S} z d S\).
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...
4. Let S be the part of upper cone == (2x +2y)" lies below 2 =1+2. (a) Find a parametric representation for S. (b) Find an equation of the tangent plane at point ( (c) Find the area of S. 1,2).
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 2
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...
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 (surface area) of the part of the hyperbolic paraboloid z = y2 - x that lies between the cylinders x + y2 = 1 and x² + y2 = 4
4. Find the surface area of part of the paraboloid z =x2 + y2 cut of by the plane z = 4.
Find the area of the surface. 7. The part of the hyperbolic paraboloid z = y2 – x? that lies between the cylinders x + y² = 1 and x² + y² = 4
Let Surface S be that portion of the paraboloid z = x2 + y2, which lies between the planes z = 4 and z = 25. Find the Area of S.