Calculate the volume of one of the wedge-like objects formed by cutting the cylinder x²+9y²=a² with the planes z=0 and z = mx.

Q: 3. Find the volume of the object cut from the cone z = Vx² + y² by the plane z = 1.

A: The volume of a solid can be obtained by considering a small volume element and integrating within…

Q: Find the volume of the solid bounded by the ellipic paraboloid z = 1 + 2x? + 3y°, the planes x = 2…

A: Given query is to find the volume of the solid.

Q: Find the volume of the solid that lies under the plane 3x + 2y + z = 12 and above the rectangle. R=…

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Q: What is the volume of the solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y…

A: Given,  The solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y = x2 and x = y2

Q: Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic…

A: Solution: In the plane z =0 the two cylinders intersect x=±1, y=0y=1-x2 meets the y-axis at…

Q: Find the volume of the solid S whose base is the disk bounded by the circle x^2 + y^2 = r^2 and the…

A: Solution is given below:

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: Question included in image

A: Find the volume of the wedge cut from the first octane by the cylinder and the plane

Q: Find the volume of the wedge cut from the first octant by the cylinder x? + y² = 1 and the plane 2x…

A: We have to find the volume of the wedge cut from the first octant by the cylinder x2+y2=1 and the…

Q: Find the Volume cutoff from the cylinder x2 +y2 = 9 by the planes z = 0 and z = 5.

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Q: Find the surface area of the solid of intersection of the cylinders  x2 + z2 = 9  and  y2 + z2 = 9

A: To find the surface area of the solid

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 1+ 3x? + 5y², the planes x = 2…

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Q: Find the volume of the solid that lies within both the cylinder x+y = 4 and the %3D sphere x+y+z2 =…

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Q: Find the volume of the solid bounded by the paraboloid z = 16 – 2? – y, the cylinder 2 + y? 8 and…

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Q: ^2) and

A: In this question, the concept of Spherical Coordinates is applied. The Cartesian Coordinate system…

Q: Find the volume of the smaller region cut from the solid sphere ρ≤ √2 by the plane z = 1.

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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 volume of the solid cut from the square column |x|+ |y|<=1 by the planes z = 0 and 3x +…

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Q: Find the volume of the wedge cut from the cylinder x 2 +y 2 =9x 2+y 2 =9 by the planes z=0and z=y…

A: Solution :

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: Find the volume of the wedge-shaped region on the figure below contained in the cylinder x2 + y2 =…

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Q: Find the volume of the solid enclosed by the paraboloids z z = 18 – 4 (x2 + y²). 4 (x² + y²) and

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Q: Find the volume of the solid bounded by the paraboloid z = 28 – x2 – y², the cylinder x2 + y² = 14…

A: Given- Praboloid,z=28-x2-y2Cylinder: x2+y2=14 To find : Volume of solid

Q: Find the volume of a solid bounded by the paraboloid z² + y² = 4x and the plane x = 5

A: Given Data: Equation of Paraboloid: z2+y2=4x  ........... (1) Plane x=5

Q: Find the volume of a solid enclosed by the parabolic cylinder y = x^2, the planes z = 0 and y + z =…

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Q: Calculate the volume of the solid limited by the given surface 3x+2y-z=6 and the conventional…

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Q: Find the volume of the solid that is enclosed by the cone z = x² + y² and the sphere x² + y² + z² =…

A: Given: Equation of cone z=x2+y2 Equation of sphere x2+y2+z2=2

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 1 + 5x + 4y", the planes a = 5…

A: To get the volume of the region which is bounded by the given equations we can use the double…

Q: Find the volume of the solid bounded by the paraboloid z = 2 – 4x? – 4y? and the plane z =

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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: Find the volume of the solid bounded by the plane 10x + 8y + 8z = 9 in the first octant. Leave your…

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Q: Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic…

A: Given equations are, y=1−x2y=x2−1 Equation of planes are, x+y+z=24x+2y−z+14=0

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

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Q: 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 bounded by the ellipic paraboloid z =1+5x2 +3y2, the planes I = 2 and y…

A: We need to find the volume of the solid bounded by the elliptic paraboloid z=1+5x2+3y2, the planes…

Q: Find the volume of the solid that lies under the plane 4x+6y-2z+15=0 and above the rectangle…

A: Consider the given plane

Q: Find the volume of the solid bounded by the ellipic paraboloid z = 2 + 4x² + 2y², the planes a = 3…

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Q: find the volume,The region cut from the solid elliptical cylinder x2 + 4y2<=4 by the xy-plane and…

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Q: Find the volume of the solid enclosed by the parabolic cylinders y = 1 – x², y= x² – 1, and the…

A: We need to find volume.

Q: Find the volume of the region D enclosed by the region cut from the cylinder x2 + y2 4 by the plane…

A: Find the limit of the x, y and z:

Q: Find the volume of the solid bounded by the ellipic 4 + 5x² + 3y², the planes x paraboloid z = = 2…

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Q: Find the volume of the solid bounded by the ellipic paraboloid z =1+5x² + 3y², the plane ¤ = 2 and y…

A: the formula used to find the volume of the region bounded by the surface, the planes, and the…

Q: Find the volume of the solid by subtracting two volumes, the solid enclosed by the parabolic…

A: Here the objective is to find the volume of solid enclosed by the parabolic cylinders

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 that lies under the plane 4x + 6y – 2z + 19 = 0 and above the rectangle…

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Q: Find the volume of the wedge cut from the first octant by the cylinder z=63-7y and the plane x+y=3

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Q: Find the volume of the solid bounded by the elliptic paraboloid z = 5 + 4a² + 3y?, the planes a and…

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Q: Find the volume of the solid bounded by the elliptic paraboloid z = 2 + 5x² + 4y², the planes x = 4…

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Q: Find the volume of the solid that lies under the double cone z2 = 4x2 + 4y2, inside the cylinder x2…

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