The circular cross-section of the cylinder, y + z? = 4, can be obtained by cutting it along any plane parallel to None of these O yz-plane ху-plane O xz-plane

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the…

A:

Q: Find the area of the surface x2 + y2 - z = 0 that is cut from above by the plane z = 4

A: Surface is given by x2+y2=z Area=∫∫R2x2+2y2+1dA       =∫∫R4x2+4y2+1dA Let x=rcosθ and y=rsinθ…

Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

A:

Q: Find the surface area of the part of the spherex +y² +z = 16 that lies above the plane z = 2.

A:

Q: Evaluate ze dV, where E is the portion of the ball centered at the origin of radius 5, x + y+< 25…

A: Given Where E is portion of the ball centered at origin, radius 5 and lies in first octant. In…

Q: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: Find the plane x/a + y/b + z/c = 1 that pass-es through the point (2, 1, 2) and cuts off the least…

A:

Q: The axis of symmetry of the cylinder is parallel to the z-axis. х-ахis. O y-axis.

A:

Q: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z &gt; 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z &gt; 0, by the cylinder x2 + y2 = 2y

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

A: We have to find volume.

Q: Give a parametrization, including the appropriate u- and v-bounds, for the portion a cylinder of…

A:

Q: Compute the surface area of the portion of the hyperboloid x² + y? -? = 64 between z = 7 and z = 8.

A:

Q: S how that the line af intesection of the Planes and 5x-2y-Z=0 X+2y-22= 5 is Paralkel to thelime メ+3…

A:

Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

A:

Q: how by integration that the centroid of a uniform semi-circular lamina of radius a from ne centre is…

A:

Q: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

Q: Find the volume of a parallelepiped whose edges are ä = 7i+5j-k, 6-j+4k and e= 4i-3j+6k %3D

A:

Q: Find the area of the portion of the cylindrical surface y = 4 - x2 in the first octant that is…

A:

Q: Evaluate the integral xyzdV where E lies between the spheres with radius 2 and 4 and above the cone…

A: Using spherical coordinates,

Q: 4. Find each volume. (a) A solid is being bounded by paraboloids z = 2x² + y? and z = 27 – x² – 2y?.…

A: We have to find the volume  from the given condition

Q: Show that the volume of a spherical block can be approximated by ∆V ≈ ρ2 sin ϕ ∆ρ ∆ϕ ∆θ.

A: Suppose x,y,z is a point at fixed distance from the origin in the 3D-space.

Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

Q: Use Stoker Cur theorem to evaluate. IF - ds S Where F= of radius I with x ] +ya³k ands is the +yx³k…

A: Given That  ∬Curl F →·dS→ F→=yi-xj+yx3k To Find: evaluate  ∬Curl F →·dS→  using strokes theorem

Q: Find the Largest open rectangle in the plane in which the hypotheses of Existence and uniqueness…

A: Answer

Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

A:

Q: Find the area of the region cut from the plane x+4y+8z=9 by the cylinder whose walls are x=y2 and…

A: Given, x+4y+8z=9 x=y² x=18−y² Therefore, The surface is  f=0 with f= x+4y+8z-9

Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: The solid in the first octant bounded by the coordinate planes, y+ z = 4, and x = y.

A: The objective is to find the volume for y+z=4,x=y The volume of the integral formula is,…

Q: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…

A: Given that  Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle

Q: Find a formula for the distance from the point P(x, y, z) to the a. xy-plane . b. yz-plane c.…

A: a) xy plane is given by z=0 We have to find distance of (x,y,z) from z=0

Q: Calculate the volume under the elliptic paraboloid z = 4x² + 6y2 and over the rectangle R = [-2, 2]…

A:

Q: Find the distance between the planes 4x + 5y + z = 25 and 4x + 5Y + z = 53. %3D

A: Explanation of the solution is given below....

Q: Find a parametrization of the circle of radius 7 with center (5, 3, 9) in a plane parallel to the…

A:

Q: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

A:

Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: + 1 -оу-х -oy=x2

A:

Q: A right cylinder of radius r is inscribed in a hollow sphere of fixed radius a. The

A: Given, a right cylinder of radius 'r', is inscribed in a hollow sphere of fixed radius 'a'. The…

Q: Find the average z-coordinate of points in a hemisphere of radius 8 centered at the origin with its…

A: We have to find the average z coordinate of the hemisphere of radius 8 centered at origin with base…

Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

A:

Q: Find the surface area of that part of the plane 8x + 9y + z = 8 that lies inside the elliptic…

A:

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A:

Q: Find the area of the part of the plane defined by 3z + 2y + z 12 that lies in the first octant.

A: Given equation of plane :  3x+2y+z= 12

Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Calculate the volume under the elliptic paraboloid z=3x2+7y2 and over the rectangle R=[−2,2]×[−4,4

A: Explanation: We know that,  Volume =∬zdydx By using the double integral concept, the volume of the…

Q: Use Pappus’s Theorem for surface area and the fact that the sur-face area of a sphere of radius a is…

A:

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

A:

Q: Find the surface area of the part of the plane z = 4 + 6x + 2y that lies above the rectangle [1, 4]…

A:

Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

A: