9. Use a surface integral to show that the surface area of a right circular cone of radius R and height h is RVh²+R². (Hint: Use the parametrization x=rcos0, y=rsine, z = =r, for Osr≤R and 0≤0 ≤2.)

Q: Find the average squared distance between the origin and thepoints on the paraboloid z = 4 - x2 -…

A: Given: Paraboloid: z=4-x2-y2, z≥0 To find the Average squared distance.

Q: Use explicit description of the surface to evalue the integral.

A: Step 1: it is provided that, there is a surface integral∫∫(x+yz)dSwhere S:z=−x−2y+4 on…

Q: Let S be the surface of the sphere of radius 6 centered at the origin, and let F(z, y, 2) =…

A: Let S be the surface of the sphere of radius 6 centred at the origin. Let F(x,y,z) = x3zi…

Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: Find the area of the surface generated by revolving the curve about each given axis. x = 2t, y = 9t,…

A: x= 2t, y= 9t, 0<= t <= 3

Q: Q4\Find the surface area of the plane z = x2 + y² from z=4 to z=9? %3D

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Q: nd the area of the surface generated by revolving the curve x= Osys2, about the y-axis. 3

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Q: Find the area of the surface obtained by rotating the curve y = x², 0 < x< 1, about the y axis.

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Q: Find the area of the surface obtained by rotating the curve y = √5x from x = 0 to = 4 about the…

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Q: Find the area of the surface defined by x + y + z = 1, x2 + 2y2 ≤ 1.

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Q: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

A:

Q: Let S be the surface given by the first octant part of the paraboloid z=4-x^2-y^2. Find the area of…

A: We need to determine the surface area of the surface bounded by the paraboloid: z=4-x2-y2 in the…

Q: Explain how to set up a surface integral given that you will project the surface onto the xz-plane.

A: Let the provided surface is S and the function is f whose integral over surface S is to be find.…

Q: Find the area of the surface generated by revolving x=t^2      y=2t.     t∈0,4) around the x-axis

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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? <…

A: