Find the area of the part of the sphere r? + y + z² = 4 that lies within the first octant and inside of the cylinder r² + (y – 1)? =1.

Q: the volume of the solid enclosed by the paraboloids z = = 16 (x? + y?) and z = 18 – 16 (x² + y²

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Q: Find the volume of the solid above the cone z = Vx² + y? and below the paraboloid z = 20 – x² – y?

A: Given For the given region, the paraboloid z=20-x2-y2 is the upper surface, and the cone z=x2+y2 is…

Q: Find the area of the surface. The part of the paraboloid x = y? + z² that lies inside the cylinder…

A: We have to find the surface area according to given information

Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y² – x² + 2 and above…

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Q: Find the area of the paraboloid x? + y +z² = 2 by the plane y = 0.

A: We need to calculate the area of the paraboloid x2+y+z2=2 that is cut by the plane y=0. The equation…

Q: Compote the volume of a reoion inside the Sphere x" +Y? +z² =4 ond between two sheets of the…

A: We have to find V0, V0 = Volume of sphere - V1-V2And from Symmetry we know that V1 = V2⇒V0 = Volume…

Q: Find the volume of material cut from the solid sphere r2 + z2 <=9 by the cylinder r = 3 sin u.

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Q: The circular cross-section of the cylinder, y + z? = 4, can be obtained by cutting it along any…

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Q: Find the surface area of the portion of the paraboloid z = 9- r - y? between the cylinders r?+ y? =…

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Q: Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder x² + y?…

A: Part of the plane is z = 5 + 7x + 2y, so this is given in terms of f(x,y). If part of the plane is…

Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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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 volume of the solid that lies under the hyperbolic paraboloid z=3y^(2)−x^(2)+4 and above…

A: The volume of the solid is determined by

Q: Evaluate the double integral V1 + 4x² + 4y²dA, where D is the region inside the circle x + y? = 25…

A: We have to find area of the region bounded by the circle given in the first quadrant of the plane.

Q: Find the volume of the solid that lies inside both the cylinder x² + y² = 16 and the sphere x² + y²…

A: Given cylinder and sphere x2+y2=16x2+y2+z2=36 clearly, Here we need to find volume inside both…

Q: Let S be the part of the hyperbolic paraboloid z = x2- y2 located between the cylinders x2 + y? = 1…

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

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Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder a² + y?…

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Q: The area A(E) of the surface E that is the part of the surface z = xy that lies within the cylinder…

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Q: Compute 3xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: Find the area of the part of the cylinder y2 + z2 = 4 in the first octant, cut out by the planes x =…

A: Given. We are given a cylinder in the first octant.. y²+z² = 4 We need to find the volume of the…

Q: Find the surface area of the part of the plane z = 5 + 4x + 3y that lies inside the cylinder 22 + y?…

A: We have to find surface area of the plane z=5+4x+3y that lies inside the cylinder x^2+y^2=16.

Q: Q2 (a) Find the volume under the surface z = 3x³ + 3x?y and over the rectangle R = {(x, y):1 < x <…

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Q: * Find the surface area of the part of the plane 2x + 5y + z = 2 that lies inside the cylinder x? +…

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Q: 8. Find the surface area of the part of the sphere x2 + y? + 22 : = 4z that lies inside the…

A: The solution is given as

Q: Find the area of the part of the sphere x2+y2+z23D 9z that lies inside the paraboloid z =r+y?. a.…

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Q: nd the volume of the solid bounded by the paraboloid z = 32 – x² – y², the cylinder r² + y? = 16 and…

A: The solution are next step

Q: Show that the volume common to the surfaces 2 p2+z=4ax and x+y?=2ax is (3r+8)*. 3

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Q: Find the area of the portion of the plane 3x − 3y + z = 12 that lies inside the cylinder y^2 + z^2 =…

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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 x2…

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Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: Find the surface area of the portion of the surface z = xy which is inside the cylinder p2 +3? = 9.

A: It is given that the portion of the surface is z=xy=fx,y. The surface area of the surface is…

Q: Find the area of the surface . The part of the paraboloid x = y? + z? that lies inside the cylinder…

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Q: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: Find the surface area of the part of the hyperbolic paraboloid z = y? –x² that lies between the…

A: Given The hyperboloid z=y2-x2 that lies between the cylinders x2+y2=1 and x2+y2=4.

Q: Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

A: to find:- surface area, A.

Q: Find the area of the upper portion of the cylinder x² + z? = 1 that lies between the planes x = ±1/2…

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Q: Find the volume of the ellipsoidal solid given by 4x² +4y² +z? = 16

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Q: tind the volume Of the solid bounded below the Sphere t+Z=1, above the ay-plane Cre z >o and to the…

A: To find the volume of the solid between the sphere x2+y2+z2=1, above the xy-plane and to the right…

Q: Find the surface area of the portion S of the cone z2 = x? + y², where z > 0, contained within the…

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Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 – x2 + 2 and above…

A: To find the volume of the solid that lies under the hyperbolic paraboloid  z=3y2-x2+2 and above the…

Q: Find the area of the part of the surface z = xy that lies within the cylinder x2 + y2 = 9.

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Q: Find the volume of the solid that lies under the elliptical paraboloid z = 2x2 + y? +4 and above the…

A: Given, z=2x2+y2+4 To find Volume of Solid

Q: Q2 (a) Find the volume under the surface z = 3x³ + 3x?y and over the rectangle R = {(x, y): 1 < x <…

A: Volume of the surface and surface  area using double integral

Q: Find the area of the part of the plane x + 4, y + z = 4 that lies in the first octant. 1. A = 12 2.…

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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 x2…

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Q: Evaluate T// y dV, where E is the portion of the sphere x² + y? + z² = 9 in the first octant (where…

A: Let, x=rsinθcosϕy=rsinθsinϕz=rcosθ

Q: need ASAP B. Find the area of the portion of the cylindrical surface y = 4 − x2 in the first…

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Q: Find the area of the part of Sphere x? + y? + z? = 16 that is outside the paraboloid z=16 – x² – y?.…

A: The part of the object outside another object can be obtained by first calculating the intersection…