Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z 2Rz, where R is a = positive constant. What is the area of that portion of the sphere that is inside the cone?

Q: Find the volume of the solid that lies under the elliptic paraboloid x2/9 + y2/16 + z = 1 and above…

A: Volume in xy-plane

Q: Find the volume of the solid that lies under the plane 4x + 8y − 2z + 13 = 0 and above the rectangle…

A: Find the volume of the solid that lies under the plane 4x + 8y − 2z + 13 = 0 and above the rectangle…

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: Find the volume of the solid whose base is the triangle in the xy-plane bounded by the x-axis, the…

A: Given plane z=3-x-y and the lines y=x and x=1. The objective is to find the volume of the solid…

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: (b) Calculate the volume of the tetrahedron in the first octant bounded by the plane x + 2y + 3z = Q…

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Q: Find the volume of the solid above the cone z2= 3(x2 + y2 ), z ≥ 0 and below the sphere x2+ y2+ z2 =…

A: We convert the units in spherical coordinate. The cone is given as,  The sphere is given as, The…

Q: Find the volume of the solid within the cylinder x2 + y2 = 4 that is bounded below by the xy-plane…

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Q: Find the surface area of ​​the solid intersection of the cylinders x² + z² = 1 and y² + z² = 1

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Q: Find the surface area of that portion of the surface z = V4 -x that lies above the rectangle R in…

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Q: Find the volume of the solid bounded by the paraboloids z 9 + 3x2 + 3y and z = 7 - 3x? – 3y?

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Q: Find the volume of the solid that lies under the paraboloid  z = 8x2 + 8y2, above the xy-plane, and…

A: Given  the paraboloid  z = 8x2+8y2 , above the xy-plane, and inside the cylinder  x2+y2 = 2x.

Q: Find the surface area of the portion of the cone z=ax +y within the cylinder x+y =1.

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Q: Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1 s x< 11, 0 < y 1.

A: Consider the given: z=1+2x+3y+4y2 So, area of the part of the surface: Find the first order of the…

Q: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

Q: Find the area of the surface defined by x + y + z = 1, x2 + 8y2 s 1.

A: Given,            x+y+z=1,     x2+8y2≤1

Q: Find the volume of the solid bounded by the paraboloid z = 8- 2x - 2y and the plane z = 0

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Q: Compute the surface area of the domed structure D:= {(x, y, 2) ; x² + y² + (z – 1)² = 2 ; z > 0}.

A: x2 + y2 + (z-1)2 = 2  ,  x2 + y2 + (z-1)2 = 2  ,  z ≥ 0 This equation is for sphere of radius  = 2…

Q: Q5: Find the volume of the solid bounded by surfaces z = /9- x2 - y2, and z = /25 – x2 - y² and the…

A: Given solid is bounded by Z = 9-x2-y2 and Z = 25-x2-y2 and x2+y2-z2 = 0

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: The volume of the solid bound by the two surfaces is z = 8- 3(x² +y?), z= (x² + y?)² - 2.

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Q: Find the volume of the solid below the cone z = /x² + y² and above the ring 1 < x² + y² < 4

A: The given solid lies below the cone z=x2+y2 and above the ring 1≤x2+y2≤4

Q: Find the volume of the solid bounded by the paraboloids z = 6 – x² – y? and z = 2x2 + 2y2.Use polar…

A: Given paraboloids z=6-x2-y2 and z=2x2+2y2 We have to find volume of the solid by the given…

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

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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: Find the volume of the solid that lies within the surface x² + = 7z, and in between the cones z =…

A: To find the volume of the solid that lies within the surfaces x2+y2+z2=7z, and in between the cones…

Q: (c) By using double integrals, find the surface area of plane 2x + 5y + z = 10 that lies inside the…

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Q: Find the volume of the solid that lies under the elliptic paraboloid x2/9 + y/16 + z = 1 and above…

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Q: Verify Stoke 's Theorem for F = (x² +y – 4) î + 3 xyj + (2 xz + z²) k over the surface of hemisphere…

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Q: Find the volume of the solid that lies within the sphere x² + y + z² = 81, above the xy plane, and…

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Q: The solid in the first octant bounded by the coordinate planes, y+ z = 4, and x = y.

A: The objective is to find the volume for y+z=4,x=y The volume of the integral formula is,…

Q: Find the area of the surface defined by z = xy and x2 + y2 < 7.

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Q: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: Find the volume under the paraboloid  z = 4x2 + 4y2,  above the xy-plane, and inside the cylinder…

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Q: Find the volume of the solid that lies under the surface z = 4x + 5y + 20 and above the region D in…

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Q: Find the surface area of the part of z = xy that lies in cylinder given by x2 + y2 =  1

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Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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Q: 8. Find the volume between the cone z = Vx² + y² and the plane z = 10+ x above the disk x2 + y² < 1.

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Q: Find the volume of the solid enclosed by the cone z = √(x2 + y2) between the planes z = 1 and z = 2.

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Q: Find the volume of the solid bounded by the sphere x2+y2+z2=6 and the paraboloid x2+y2=z.

A: Given Data The equation of the sphere is x²+y²+z²=6. The equation of parabola is x²+y²=z.   Let,

Q: Find the volume of the solid that lies under the plane 4x + 6y – 2z + 19 = 0 and above the rectangle…

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

A: Consider the formula for the surface area.Find Zx and Zy by partial differentiation .

Q: Find the volume of the solid bounded by the paraboloids z = – 5 + 2x? + 2y² and z = 9 – x2 – y²

A: The solid is bounded by the paraboloids,  z=-5+2x2+2y2 . . . .. 1&amp; z=9-x2-y2 . . . . . .2 Use…

Q: 1. Find the surface area of the cone z = √x² + y² that lies between the plane y = x and the cylinder…

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Q: Find the valume of the Solid bounded by the para boloid そ- 28-x2 152the cylinder x2+y?= 24 and xy-…

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Q: Find the average height of the (single) 34. Average height of a cone cone z = Vx² + y² above the…

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Q: Find the volume of the solid enclosed by the cone z = sqrt(x2 + y2) between the planes z = 1 and z =…

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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 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: Q5: Find the volume of the solid bounded by surfaces z = /9 - x2 - y2 , and z = /25 - x2 - y? and…

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