Let Surface S be that portion of the sphere x2 + y2 + z2 = 9, which is above the plane z = 1. Parametrize this surface and write your final answer in vector function notation.
Let Surface S be that portion of the cylinder x2 + y2 = 9, which lies between the planes z = y and z = 6. a.) Sketch the Surface S. b.) Parametrize the Surface S. c.) Evaluate the following Surface Integral: ∫∫(y-z)dS
1 point Let S be the portion of the sphere z2 + y2 +z2-4above the cone z-cVz2tr where c-1N3 Find the surface area of S Surface Area 2sqrt3 Evaluate the surface integral 1 point Let S be the portion of the sphere z2 + y2 +z2-4above the cone z-cVz2tr where c-1N3 Find the surface area of S Surface Area 2sqrt3 Evaluate the surface integral
Let P = (0,0, 2)and let S be the unit sphere with equation x2 + y2 + z2 = 1.The collection of points on the sphere where the tangent plane of the sphere contains the point Pforms a curve. Parametrize this curve.
Find the area of the surface. The portion of the sphere x2 + y2 + z2 = 625 inside the cylinder x2 + y2 = 400 d Help? Read It Talk! Talk to a Tutor Tutor
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...
QUESTION 5 Let the surface S be the portion of the cylinder x2 + y2 4 under z 3 and above the xy-plane Write the parametric representation r(z,0) for the cylinder x2 +y2 4 in term of z (a) and 0 (2 marks) Based on (a), find the magnitude of llr, x rell for the given cylinder (b) (6 marks) 1 1+ (e) Evaluate z dS for the given S (8 marks) Hence, use the divergence theorem to evaluate f,...
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6 and below the paraboloid z = 4 - x2 - y2 as shown in Figure Q5(a) below: Z=4-x-y? x2 + y + z = 6 Figure Q3(a) (i) Find the equation of the projection of Won the xy-plane. (ii) Compute the volume of W using polar coordinates. [16 marks] (b) Using double integral in polar coordinates, compute the following: $$*** (2x+3y) dedy [7 marks]...
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.
Find the volume of the solid bounded on top by sphere x2+y2+z2= 9 , on the bottom by the plane z = 0, around the side by the cylinder x2+y2= 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.