(a) Find the surface area of the plane 3x +2y + z = 6 that lies in the first octant.

Q: Find the surface area of the portion of the paraboloid given by the equation z = 1– x2 – y² that is…

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Q: Evaluate the surface integral. x dS, S is the part of the plane 16x + 8y + z = 16 that lies in the…

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Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

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Q: 5. Use polar coordinates to find the volume of the solid enclosed by the hyper- boloid –r² – y² + z²…

A: To obtain the limits of integration for z, rewrite the equation -x2-y2+z2=1, and find z.…

Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Find the area of the ellipse cut from the plane z = cx (c a constant) by the cylinder x2 + y2 = 1.

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Q: EXAMPLE 2 Find the area of the part of the paraboloid z = x + y' that lies under the plane

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Q: 18. The volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane z = 6

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Q: Find the area of the surface. The part of the hyperbolic paraboloid  z = y2 − x2  that lies between…

A: In the question we have to find the value of area enclosed by the function of given figures.

Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x²…

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Q: Evaluate the surface integral. ∫∫sxdS, S is the part of the plane 6x+3y+z=6 that lies in the first…

A: The plane has intercepts at (1,0,0), (0,2,0), (0,0,6). The parameterize the surface S by. where

Q: Find the area of the surface. The surface cut from the bottom of the paraboloid z = x2 + y2 by the…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 16 that lies above the plane z =…

A: The objective is to find the area of the surface of the part of the sphere x2+y2+z2=16 that lies…

Q: Find the area of the surface cut from the paraboloid x2 + y + z2 = 2 by the plane y = 0.

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Q: Find the area of the surface. The part of the plane  x + 2y + 3z = 1  that lies inside the cylinder…

A: Compute the partial derivative as follows.

Q: Evaluate the surface integral. /| xz ds, S is the part of the plane 2x + 2y + z= 4 that lies in the…

A: We need to find surface integral.

Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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Q: Evaluate the surface integral: x dS,  S is the part of the plane  12x + 6y + z = 12  that lies in…

A: From the given statement, the plane is 12x + 6y + z = 12 and it is lies in the first octant.

Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: Find the area of the surface. The part of the paraboloid z = 1 – x² – y2 that lies above the plane z…

A: Givenz=1-x2-y2z=-2Suppose the surface is defined byz=f(x,y) for x∈R, then the area of the surface is…

Q: Integrate G(x, y, z) = xyz over the surface of the rectangular solid cut from the first octant by…

A: Given: G(x,y,z)=xyz We have to integrate G(x,y,z) over the surface of the rectangular solidcut from…

Q: Find the area of the part of the paraboloid z=x² + y² that lies under the plane z=9.

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Q: Find the area of the surface of the part of the plane 3x + 2y + z = 6 that lies in the first octant.

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Q: Find the surface area of the paraboloid z =1-x² - y? that is above the xy-plane.

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Q: 3. Use polar coordinates to find the surface area of the paraboloid z = x² +y² – 5 that lies below…

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Q: Find the area of the part of the plane 3x + 3y + z = 9 that lies inside the cylinder x2 + y2 = 25.

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Q: Find the area of the surface cut from the paraboloid x2 + y2 - z = 0 by the plane z = 2.

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

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Q: 29. Using Pappus' theorem, the value of the y-coordinate of the centroid of a uniform semi-circular…

A: Pappus centroid theorem states that the volume V of a solid of revolution generated by revolving a…

Q: 3) Find the surface area of the portion of the paraboloid z = x2 + y2 below the plane z = 1. %3D

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Q: Integrate g(x,y,z) = x + 5y + z over the portion of the plane 4x + 8y + z = 8 that lies in the first…

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Q: Find the surface area of the plane 3x + 2 y + z = 6 that lies in the first octant.

A: The surface area of the plane z=f(x,y) is given by the formula                          S=∬D…

Q: The region cut from the solid elliptical cylinder x2 + 4y2≤ 4 by the xy-plane and the plane z = x +…

A: Given that, z=x+2 , x2+y2≤4

Q: Find the centroid of a thin, flat plate covering the “triangular” region in the first quadrant…

A: Consider the given curve.

Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

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Q: Find the area of the surface. The part of the plane 3x + 5y + z = 15 that lies in the first octant

A: Given plane,  3x+5y+z=15Intercepts of the plane axis are  x=5, y=3, z=15

Q: Find the area of the finite part of the paraboloid  y = x2 + z2 cut off by the plane y = 4.

A: To find the area of the finite paraboloid y=x2+z2 cutt off by the plane

Q: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

Q: Find, by using polar coordinates in R2, the volume of the region bounded by the paraboloid z = 20 –…

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

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Q: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

Q: Find the area of the surface. The part of the plane 2x + 4y + z = 8  that lies inside the cylinder…

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Q: Integrate G(x, y, z) = x + y + z over the surface of the cube cut from the first octant by the…

A: Definition used:

Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…

Q: 1) Find the volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane Z = 8.

A: The main objective is to find the volume of solid that lies between the paraboloid z=2x2+2y2 and the…

Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

A: we have to find area of the portion of plane .and coverting the problem in polar coordinate makes it…

Q: 4. Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = 2r and y…

A: The given problem is to find the centroid of the thin flat plate covering the region enclosed by…