Use Pappus’s Theorem for surface area and the fact that the sur-face area of a sphere of radius a is 4pai a2 to find the centroid of the semicircle y = sqrt(a2 - x2).

Q: Evaluate the surface integral LL 6xzdS where S is the part of the plane 2x + 2y + z = 4 that lies in…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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

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Q: Use a computer algebra system to find the approximate surface area of the solid generated by…

A: To find the surface area using the computer algebra sysytem

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

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Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? O 0 02 Ο ΝΑ x-coordinate of the…

A: Solution is given below:

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 area of the part of the plane  z = ax + by + c  that projects onto a region in the…

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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 volume of the shaped body bounded by the z = 3x2 + 3y2 and          z = 4 - x2 - y2…

A: We have to Find the volume of the shaped body bounded by the z = 3x2 + 3y2 and        z = 4 - x2 -…

Q: Evaluate the surface integral xyzdS where S is the part of the plane z = 1 + 2x + 3y that lies above…

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Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

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Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabola y2 = x and the…

A: Given information:

Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: Explain why the explicit description for a cylinder x2 + y2 = a2 cannot be used for a surface…

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Q: Find the surface area of that part of the plane 9x + 6y + z = 4 that lies inside the elliptic…

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Q: Use the Divergence Theorem to evaluate the surface integral (2x^2 + 3yz + 4xz) dS where S is the…

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Q: Calculate the surface area x2+y2+z2=25, between the z=1 and z=4 planes

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Q: Find the surface area of the portion of the surface x2- 2 In a+ V15 y - z = 0 above the rectangle 1…

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Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: Find the centroid of the area of a trapezoid that has two equal slanting sides, a 6 cm base and a 3…

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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 centroid of a lamina enclosed between the circles of radius 1 and 2 centred at the origin,…

A: Consider the diagram of the lamina as per given information, The centriod of the lamina is defined…

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 the centroid of the surface formed by the revolution of cardioid r = a(1 + cose) about the…

A: Given equation of cardioid, r=a1+cosθ Let the centroid be x,y.

Q: Find the area of the surface generated by revolving x = t+2/3, y =+2/3t+1, -2/3 sts2/3 about the…

A: Find the area of the surface generated by revolving the graph of the following parametric equation…

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: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

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Q: Calculate the points of intersection of the curves x² = 4y and bn=) = y 29vaus at newed biloa gris 1…

A: Centroid: The centroid or centre of mass of a region bounded by the curves is the point where the…

Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

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Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

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

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Q: Find the centroid of the plane area bounded by the parabola y = 6x - x² and the line y = x

A: To Find: The centroid of the plane area bounded by the parabola y=6x-x2 and the line y=x

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: Find the centroid by revolving the given plane area about the indicated axis y^2=5-x, x=0 ; about…

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Q: Find the centroid of the semicircular area inside x2+ y2 = a2 with y ≥ 0. Show the graph for it.

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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 the surface area obtained by rotating y = V9 – x2 ,-2sxs-1 9– x² -2sxs-1

A: Given,             y=9-x2 , -2≤x≤-1

Q: Find the surface area of the portion of the cone z = x2 + y2 in between the planes z = 3 and z = 4.

A: The area of the surface z=fx,y above a region R of the xy-plane is given as follows.…

Q: Find the area of the surface obtained by rotating thecircle x2 + y2 = r about the line y =r.

A: We have to find the area of the surface obtained by rotating the circle x2 + y2 = r about the line y…

Q: Find the surface area obtained by rotating y = V9 – x² -2sxs-1

A: As we know that; The expression for the area of surface rotating about the x-axis. S=2π∫abfxf'x2+1dx…

Q: Use polar coordinates to find the volume of the solid below the paraboloid z=75−3x2−3y2z=75−3x2−3y2…

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Q: find the coordinates of the centroid of the plane area bounded by the parabola y=4-x^2 and the…

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Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: Find the area of the elliptical region cut from the plane x + y + z = 1 by the cylinder x2 + y2 = 1

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Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

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

A: From the given statement, the plane is 5x + 3y + z = 15 and it is lies in the first octant.

Q: Find the area of the surface generated by revolving the region bounded by, 1 + 6 y 1<x < 3 16x4…

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