O Find the volume of solid in the first octant bounded by the co- ordinate planes, the planes x-3, and the parabolic cylinder z-4-y?

Q: O Find the volume of the solid under the surface z = xy and above the triangle with vertices (1, 1),…

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Q: 4. Find the volume of the region bounded above by the paraboloid z = x? + y? and below by the…

A: (4) Consider the provided question, According to the provided question, draw the graph of the given…

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

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Q: 3. Find the volume of the tetrahedron in the first octant that is bounded by the three coordinate…

A: Given the equation of the plane, z=5-2x-y  ⋯⋯(1) Rewriting equation (1), 2x+y+z=5  ⋯⋯(2) At z=0,…

Q: Q8-Find the volume in the first octant bounded by the plane x+z=1 & y+2z =2?

A: The solution is given as

Q: Find the volume of the solid that is bounded on the front and back by the planes x = 1 and x = 4, on…

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Q: Find the volume of the solid bounded by the paraboloids z= 8+22 +2y and z 9-z-y

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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 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 volume between the surfac x²y, and the rectangle in the xy 2 = plane given by 2 < x <…

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Q: Find the volume of the paraboloid, z = 9 - x² - y², that lies inside the cylinder x² + y² = 4.

A: It is seen that the paraboloid and cylinder both are extended upto negetive infinity of along z…

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: (b) Find the volume under the paraboloid z-x+y above the triangle enclosed by the lines y=x,x-0 and…

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Q: Find the volume of the tetrahedron bounded by the plane z=4-4x-2y and the coordinate planes. I

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Q: 25. Find the volume of the solid that is enclosed by the cone z = /x² + y² and the sphere x² + y² +…

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Q: Find the "volume" of the four-dimensional pyramid bounded by w +x+ y+z-1=0 and the coordinate planes…

A: The volume of the four dimensional pyramid is given by, V=∫v1 dv   =∫dzdydxdw. The boundaries are…

Q: Q2 Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x =…

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Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y…

A: We need to evaluate volume.

Q: Find the volume of the solid below the paraboloid z =(9-x-), above the xy-plane and outside the…

A: Here, z=129-x2-y2

Q: Find the volume of the given solid. Under the surface  z = 9xy  and above the triangle with…

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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: 12. Find the volume of the solid bounded by the cylinder r2 + y² = 4 and the planes z = 0 and %3D y+…

A: The bounds are 0≤z≤3-y, -4-x2≤y≤4-x2 and -2≤x≤2.

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

A: Please see the explanation below

Q: 9. Find the volume of the solid wedge cut from the first octant, bounded by the three coordinate…

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Q: Find the volume of the region bounded above by the elliptical paraboloid z= 6-2x - 2y and below by…

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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 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 given solid. Under the surface z = 6xy and above the triangle with vertices…

A: Given: z=6xy A triangle with vertices (1,1),(4,1),(1,2)

Q: 3. Find the volume of a solid enclosed by the parabolic cylinder y = x², the planes z = 0 and y +z =…

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Q: 6. Find the volume inside the paraboloid z = 9-x² - y², outside the cylinder x² + y² = 4, above the…

A: Relation between rectangular and polar coordinate  x=rcosθy=r sinθx2+y2=r2θ=tan-1yxdxdy=rdrdθ

Q: If the region that lies inside the cardioid r = 1+ cose and outside the cirele r = 1 is the base of…

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Q: 1. Find the volume of the solid that lies under the plane 3x + 2y + z = 12 and above the rectangle…

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Q: Q2 (a) Find the volume under the surface z = 3x3 + 3x2y and over the rectangle R = {(x,y): 1 < x<…

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Q: 7. Find the volume and centroid generated by revolving the given plane area about y^2=4x, x=4; about…

A: Given that - y2 = 4x, x = 4; about x = 4

Q: Find the volume inside the sphere (r = a) that lies between the cones ($ = n/3) and ($ = 2n/3) %3D…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: If the region that lies inside the cardioid r = 1+ cos 0 and outside the cirele r = 1 is the base of…

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Q: Find the volume of the following solid. The solid bounded by the paraboloid z= 29 - 8x - 8y and the…

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Q: Find the volume of the largest closed rectangular box in the first octant having three faces in the…

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Q: Find the volume of the given solid. Under the surface z = 7xy and above the triangle with vertices…

A: Given surface is z = 7xy  And region is above the triangle with vertices (1, 1), (4, 1) and (1, 2).…

Q: 9. Find the volume of the solid in the first octant enclosed by the surface z = x? and the four…

A: Volume = ∫02∫03∫0x2dx dy dz                 =∫02dx∫03dy ∫0x2dz…

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y…

A: Please see the attachment

Q: Find the volumes of the solids

A: We have,

Q: Find the volume of the pyramid with the base in the plane z= -5 and the Sides formed by the three…

A: To find the volume of the pyramid

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

A: To find the volume of the solid the lies under the below hyperbolic paraboloid and above the…

Q: 1) Calculate a)be the volume of the solid below the paraboloid 2+x²+(y-2)² and above the rectangle…

A: In this question, we find the volume of the solid bounded by paraboloid and base is a rectangle. we…

Q: 5) Find the volume under the paraboloid z = x² + y above the triangle enclosed by the lines y = x, x…

A: We have to find the volume of the solid.     According to our guidelines we can solve only one…

Q: Find the volume of the following regions in space. 3 The tetrahedron cut from the first octant by…

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Q: The volume of the solid enclosed by the surface z = 1/y and the rectangle 2 <r<4, 1<y<e in the…

A: We use double integral to find the volume of the solid.

Q: The volume of the solid enclosed by the surface z = x/y and the rectangle 2 <x < 4, 1 < y <e² in the…

A: