Find the area of the surface. The surface cut from the bottom of the paraboloid z = x2 + y2 by the plane z = 3

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: Find the surface area of the paraboloid z= 1 - (x2 + y?) that lies between the sphere x? + y? + z² =…

A: Given the region

Q: Calculate the surface area of the following: the cap cut from the sphere r² + y² + z² = 3 by the…

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Q: Find the surface area of the part of the paraboloid z = 9 – 2.x - 2y that lies above the %3D

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Q: Find the area of the surface. The portion of the paraboloid  z = 49 − x2 − y2 in the first octant

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Q: (b) Find the surface area of the portion of the paraboloid given by the equation z = 1- x? – y? that…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 4z that lies inside the…

A: Given sphere is x2+y2+z2=4z that lies inside the paraboloid  z=x2+y2. We have to find the area f the…

Q: B- Find the area of the ellipse resulting from the intersection of the plane x+y+z=6 with the…

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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: Find the area of the surface S where S is the cap cut from the paraboloid z = 2– x – y by the cone z…

A: Given that : z=2-x2-y2z=x2+y2 Now, to find the point of intersection , 2-x2-y2=x2+y2Put…

Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = sqrt(x2 + y2).

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Q: Find the surface area of the portion of the bowl z = 8+x² + y that lies below the plane z = 14.

A: Given, z=8+x2+y2 ,z=14 Now substitute z=14 into the given surface for finding the intersection of…

Q: Find the area of the portion of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4.

A: Given that ,  paraboloid   z=x2+y2 cylinder        x2+y2=4

Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…

A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…

Q: Find the area of the surface cut from the paraboloid x² + y² -z = 0 by the plane z = 6. The surface…

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Q: Sketch the surface created by 4.r2 + 9y? + 3622 = 36. %3D

A: Given,4x2+9y2+36z2=36 Simplify equation (i) as x29+y24+z21=1  .....(i) Intercepts along x,y,z…

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

A: Given that the part of the parabola z=1-x2 -y2 that lies above the plane z= -6 . Here we have to…

Q: • Find the area of the portion of the Sphere x² + y² + 2²² = 9 between the planes Z=1 and 2 = 0.…

A: The given equation of  plane is x2+y2+z2=9. The polar coordinates are x=rcosθ & y=rsinθ. The…

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: Identify and sketch the section of the surface at x = 0. 2y? – x + 22 = 50 Type of the surface:

A: This question is related to conic section .solve in step 2.

Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 9x +y +Z = 18 is ?

A: We want to find the volume of the tetrahedron enclosed by the co-ordinate planes, i.e. x=0, y=0, z=0…

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

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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 =…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 81 that lies above the plane z =…

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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: Sketch the surface r = 2y? + 32².

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Q: Find the area of the surface. The part of the paraboloid z = x² + y2 that lies inside the cylinder…

A: Area of the surface f(x ,y) above a region R of the xy-plane is given by…

Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

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Q: Find the surface area of the portion of the part of the paraboloid z = 3 – x² – y² that lies above…

A: Given z = 3-x2-y2 , above the plane z=-1

Q: For the surface 4x² + y² −z = 0, classify the indicated trace as an ellipse, hyperbola, or parabola.…

A: We have been given the equation  4x² + y² −z = 0           (1)

Q: a. z? -y? -x?+ 4x= 5 by-3 = x?+z² 2

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 49 that lies above the plane z =…

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Q: Q4(a) Find the surface area of the part of the paraboloid z=10-x -y' that lies above the plane :=1.

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Q: Find the surface area of the portion of the cone 22 = 4x² + 4y? nat is above the region in the first…

A: Given: The portion of the cone is Z2=4x2+4y2 which is bounded by the line y=x and the parabola y=x2

Q: Find the area of the cap of the sphere x2 + y² + z? = 2 cut by the cone z = Vx2 + y² |3D

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Q: Find the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A: The plane z=11-3x+2y and cylinder is x2+y2=9. Obtain the partial derivatives of z=11-3x+2y:…

Q: + + Find the area of the portion of Sphere x² + y² + 2 = 9 betw= the planes Z=1 and 2 = 0. Draw

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Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

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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 surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Find the surface area of the plane ( 15x-5z+20y=35) if it is in the first ? octant

A: Solution

Q: 3. Find the area of the surface cut from the paraboloid x? + y +z = 2 by the plane y = 0.

A: Here we have to find the area of the surface cut from the paraboloid x2+y+z2=2 by the plane y=0.

Q: Which surface has the following equation? x2 – 2y = 32 O Cylinder O Plane Paraboloid Hynerboloid

A: Please refer to the image below

Q: Which quadric surface is this? y x2 Elliptic Paraboloid O Hyperboloid of Two Sheets O Elliptic Cone…

A: We have to answer the given equation is of which quadric surface.  given    we can see that its…

Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 36 that lies above the plane z =…

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Q: Identify the surface by completing the squares. x +16y² – z? – 14x + 32y + 8z = 0 O A hyperboloid of…

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