1. Find the volume of the solid in the first octant bounded above by the sphere a? + y? + (z – 5)² = 25 and bounded below by the paraboloid 2z = x? + y².

Q: Find the volume of the solid below the paraboloid z=2(4-x² -y"), above the xy-plane and outside the…

A: Given: z=24-x2-y2   Since if it is above the xy-plane then ⇒…

Q: 1) Find the volume of the solid bounded by the poraboloid ze40-x-y, the cylinder xry2-20 and E) too…

A: Given that, Paraboloid is, z = 40 - x2 - y2 and cylinder is, x2 + y2 = 40 We have to find volume…

Q: Find the volume of the solid that lies under the paraboloid == x² + y²₁ above the XY-plane, and…

A: Here integral transformed from cartesian to cylindrical co ordinate system . So 1st we need to know…

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 volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above…

A: The volume of the enclosed region under the, hyperbolic paraboloid z = f(x,y) and above the…

Q: A) Evaluate the triple integral ydV, E = 0, where E is the solid region bounded by the cylinder 4 =…

A: Given

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

A: Integral

Q: 39. Find the volume of the solid lying under the elliptic paraboloid x²/4 + y²/9 + z R = [-1, 1] ×…

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

A: Given the elleptic paraboloid x2/9 + y2/16 + z = 1  And rectangle R = [-1, 1] x [-3, 3] We have to…

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 E whose boundaries are given coordinates. E is located inside the…

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Q: Find the Volume of the Solid that lies under the paraboloid z=x2 +y2 above the XY-plane, and inside…

A: To change the coordinates into polar coordinate:

Q: 1. Find the volume of the solid bounded by the cylinder æ² + y² = 4, the plane z = 0, and the plane…

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Q: Find the volume of the solid bounded by the paraboloids z = - 5 + 2x? + 2y² and | = 6 – æ² – y?

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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 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: 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: Set up the integral [ s (x, y,z)dV six different ways where E is the solid in the first octant…

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Q: ) Find the volume of the solid enclosed between the paraboloids z = z = 6 – 2.x2 – y². x² + y? and -

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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.

A:

Q: 18 4 (a22) Find the volume of the solid enclosed by the paraboloids z 4 (x y and z=

A: Given

Q: 7.3 5. Use the shell method to set up and evaluate the integral that gives the volume of the solid…

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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: 10. Determine the surface area of the part of z = xy that lies in the cylinder given by x² + y² = 1.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: - 9 + 3 + 3y and Find the volume of the solid bounded by the paraboloids z == z = 8 – 3x - 3y

A: To find volume of the solid bounded by the paraboloidsz=-9+3x2+3y2 and z=8-3x2-3y2

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: Find the volume under the paraboloid z = 144 – x? – y, above the - xy-plane, and inside the cylinder…

A: As per our guidelines I answered only 1st question please the remaining question post seperately.

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

A:

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: Consider the solid whose base is the region bounded by 4x? + 9y? = 36. Y 3 -3 -2 -1 -1 2 3 2 -3 1.

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

A:

Q: 3. Find the volume of the given solid. a. Under the paraboloid z = x² +y? and above the region…

A: Given: The solid is under the paraboloid z=x2+y2 and above the region bounded by y=x2 and x=y2.

Q: Consider the solid that is bounded below by the cone z = 3x2 + 3y2 and above by the here x? + y? +…

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Q: 15. Find the volume of the solid enclosed by the surfaces 2 = 0 and 2-16-2-², whose projection onto…

A:

Q: Find the volume of the given solid. Under the paraboloid z = x² + 3y² and above the rectangle R= [0,…

A: Consider the provide question,

Q: Evaluate the triple integral /|// zdV where E is the solid bounded by the cylinder y? + z² = 625 and…

A:

Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

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: 8. Show that the volume of the region bonded by the cone z = Vx² + y² and the paraboloid z = x? + y²…

A:

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

A:

Q: O Find the volume of solid in the first octant bounded by the co- ordinate planes, the planes x-3,…

A: We will find out the required volume of the solid in the first octant.

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: 3. Find the volume of the solid above the paraboloid z = x¯+y¯ –4 and under the R = {(r, 0) |1< r <…

A: We have to find the volume under conditions

Q: Compute the volume of the solid bounded by the cylinder x2 + y² = a² and the hyperboloid x2 + y? –…

A: We have to find the volume of the solid bounded the cylinder x2+y2=a2 and the hyperboloid…

Q: 4. Evaluate x²dV G where G is a solid that lies in the first octant bounded by x? + y? = 3z and z =…

A: