Set up only. The base of a solid is an elliptical region with the boundary curve 9 x 2   + 4 y 2  = 36. Cross- sections are perpendicular to the x-axis are isosceles right triangles with one leg on the base.

Q: The plane region is revolved completely about the given line to sweep out a solid of revolution.…

A: When a rectangular plane is revolved around one of the edges, the solid of revolution forms a…

Q: The base of a solid is the region in the Ty-plane bounded by the curves y = 4 – 12² and y = 0. Every…

A: According to question given that y=4-1x2y=0

Q: The base of a solid is the region bounded by the ellipse 4x2 + 9y² 36. Find %3D the volume of the…

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Q: Use cylindrical coordinates. Find the volume of the solid that lies between the paraboloid z = x2 +…

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Q: Solve parts these 2 parts of the question. Image attached.

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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: Find the surface area of the torus obtained by rotating the circlex 2 + (y - b )2 = r 2 about the…

A: Given the equation of the circle  x2+(y-b)2=r2. We need to find the surface area of the torus…

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

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Q: The region bounded by the parabola y=x2 +1 and the line y = x + 3 is revolved about x axis. The…

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Q: Use line intaral to find the aren af the surface het extends upward from the Part of the ellipse *=…

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Q: Find the points on the surface y? = 36 + xz that are closest to the origin. smaller y-value (х, у,…

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Q: Exercise 3 The quadric surface y? = 4x2 + 16z² is a: A. Elliptical paraboloid along y-axis B.…

A: Explanation of the answer is as follows

Q: Consider the solid of revolution obtained by revolving about the x-axis the region in the first…

A: To find; The volume of the solid of the revolution obtained by revolving about the x-axis by disk…

Q: tind the Uolome of the solid that lies Para boloid R:[0,1] x[ 1,3] Under the elliptic 2: 3y? tx²+2 ļ…

A: The volume of solid V=∬zdA z=3y2+x2+2 x varies from 0 to 1 y varies from 1 to 3

Q: Describe in words the region in R' represented by the equation x² + y² – 10y + z² + 2z = 0 O A…

A: we have to check the region of the given equation in R^3 is

Q: Describe the following surface V4 - (x2 + y2)

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Q: (a) Find the region enclosed R by the curves y = r - 2x +1 and y = -x² + 2x + 7. (b) Use shell…

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Q: Find volumc of the solid gcncrated the by revolving about the y-axis the region in 4y-y and 4-y x =

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Q: Find the area of the surface. The part of the cylinder y2 + z2 = 9that lies above the rectangle…

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Q: The volume of the solid generated by revolving the region enclosed by the curve y=/2x ,2 < x < 4,…

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Q: ripie the volume of the solid B that lies above the cone z = √3x² + 3y2 and below the sphere x² + y²…

A: Given- Cone: z=3x2+3y2 Sphere: x2+y2+z2=z To find the volume of the solid B that lies above the…

Q: 6. Using Second Theorem of Pappus, calculate the volume of solid of revolution when the area of the…

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Q: ind the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Find the volumes of the solids Find the volume of the solid generated by revolving the regionbounded…

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Q: The base of a solid is the region in the first quadrantbounded by the graph of y 2-r and the r-and…

A: Solution

Q: A hemisphere of x? + y? + z2 = a? is shown. A cylinder is placed such the axis of both hemisphere…

A: Surface area is given by ∬D∂z∂x2+∂z∂y2+1dA for a functionz=f(x,y) where D is the projection of the…

Q: Describe in words the region in R' represented by the equation y² + z² = 9. A ball A cyllinder A…

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Q: 1. The plane region is bounded by the parabola y2 + 2x = 16 and the line x - y = 4. Determine: a.…

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Q: Find the area of the surface generated by revolving about the 2 2 x-axis the portion of the astroid…

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Q: he cone z^2= x^2+ y^2, for z ≥0, cuts the sphere x^2+ y^2+ z^2= 16 along a curve C. That is, C is…

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

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Q: Use cylindrical coordinates to find the volume of the solid enclosed by the paraboloid z = x² + y°…

A: Given

Q: he volumes of the solids generated by revolving the regions bounded by the graphs of the equations…

A: We have to find the volume about the given lines.

Q: Find the area of the surface generated by revolving the curve x = .0sys1, about the y-axis. The area…

A: Given curve is x=y38, 0≤y≤1 We have to find the area of the surface generated by revolving the curve…

Q: (c) The solid lies between planes perpendicular to the y-axis at y = 0 and y = 2. The cross-sections…

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Q: Find the lateral surface area of the cone generated by revolving the line segment y = x/2, 0&lt;=…

A: Find the lateral surface area of cone.

Q: The figure shows the surface created when the cylinder y? + z² =1 intersects the cylinder x? + z2 =…

A: Consider the provided question,

Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

A: The surface area formula using integration is given by: In the question, we are given: Also x lies…

Q: Using Stoke's Theorem Evaluate [(2x- y)dx – yz²dy – y° zdz) where is the circlex + y = 9…

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Q: Describe the surface. x2 16 4. O cylinder O ellipsoid O cone O paraboloid O sphere Sketch the…

A: The equation represents surface of an ellipsoid

Q: Find the area of the surface. The portion of the paraboloid z = 16 - x - y in the first octant

A: The given surface is the portion of the paraboloid z=16-x2-y2 in the first octant. The surface area…

Q: Use cylindrical coordinates to find the volume of the solid enclosed by the paraboloid z = x² + y°…

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Q: Solve using Lagrange multipliers. 22. Find the points on the surface xy – z? = 1 that are closest to…

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Q: • Find the area of the surface generated by revolving about the x-axis the upper half of the ellipse…

A: IN THIS QUESTION WE HAVE TO FIND AREA FROM REVOLUTION OF A ELLIPSE.

Q: Find the surface area of the portion of the sphere x² + y? + z² = 8 that is cut out by the cone z =…

A: The objective is to find the surface area of the portion of the sphere x2+y2+z2=8 that is cut out by…

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: Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y =…

A: The Volume of a Solid of Revolution:

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 5 - x2,…

A: For the given curve- y=5-x2,              0≤x≤2 Surface area is given by- A=2π∫cdfy1+f'y2dy when it…

Q: Use traces to help identify the surface y = 9x2+25z?. O a. Hyperbolic paraboloid b. Cone O c.…

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