2. Find the volume of the region enclosed by the paraboloid z = x2 + y? and the plane z 2x.

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 = 3y² – x² + 2 and above the…

A: Integral

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

A:

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

A:

Q: Find the volume of the region bounded above by the elliptical paraboloid z = 10 + x2 + 3y2 and below…

A:

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

A:

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

A:

Q: Find the volume of the region cut from the solid sphere (x2 + y2 + z2 < 4a2) by the cylinder 40 (x²…

A: Given x2+y2+z2≤4a2x2+y2=a2

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: 3. Find the volume of the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + %3D y + 2z =…

A: Will use the triple integration to find the volume of the tetrahedron which is bounded by the given…

Q: Find the volume of the region enclosed by the cylinder x2 + y? = 2, the plane z – x+ y= 0 and the…

A: We have,

Q: Find the volume bounded below by the paraboloid z= x? + y? & above by the plane z=2y ?

A: The objective is to compute the volume below by the paraboloid z=x2+y2 and above by the plane z=2y.

Q: Find the volume of the region bounded above by the sphere x'+y +z 2 and below by the paraboloid z=…

A:

Q: Find the volume of the region enclosed by the paraboloid (x-1)²+y=z and the plane 2x+z=2.

A: To find the volume of the region enclosed by below paraboloid and the plane. x−12+y2=z and…

Q: b) Find the volume of the solid which is in the first octant and bounded between the spheres p = 1…

A: To find- Find the volume of the solid which is in the first octant and bounded between the spheres ρ…

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

A:

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

A:

Q: Find the volume under the paraboloid z = x2 + y2 above the triangle enclosed by the lines y = x, x =…

A:

Q: Find the volume of the solid bounded by the paraboloid z = 24 – x? = y?, the cylinder x2 +y² : 12…

A:

Q: Find the volume of the tetrahedron bounded by the four planes x=0,y=0,z=0, and 2x+2y+x=4?

A: The equation of the plane 2x+2y+z=4  can be rewritten in the form  z=4-2x-2y let z=0, 0=4-2x-2y…

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

A:

Q: Find the volume of the region enclosed by the paraboloid (x-1)²+y? =z and the plane 2x+z=2.

A:

Q: 5. By using suitable coordinates, find the volume of the solid bounded above by the sphere a² + y2²…

A: Introduction: Evaluation of volume of a solid in three dimensional Euclidean space is an application…

Q: Show that the volume of the region bonded by the cone z = Vx² +y2 and the paraboloid z =x² +y is…

A:

Q: 5. Find the volume under the paraboloid = -a? – y?, and above the cone z = - p² + y?.

A:

Q: d) Find the volume of the solid region bounded by the paraboloid z = 4-x² - 2y and the ху- plane

A: The above of the solid region is calculated as : ∫∫∫Ddv = V In order to calculate the volume of…

Q: Determine the volume of the region that lies under the sphere x² + y² + z² = 4, above the plane z…

A: Given: Now,

Q: Find the volume under the paraboloid z= -r - y², and above the cone : = -

A:

Q: Find the volume of the region bounded above by the paraboloid z = x² + 2y² and below by the square…

A:

Q: Find the volume of the region enclosed by the cylinder x2 + y? x² + y? + 4. = 2, the plane z – x +y=…

A: We have to find the volume of the given region.

Q: Find the volume of the solid in the first octant bounded by the cylinders x² + y? 16 , y² + 22 16.…

A:

Q: Find the volume bounded below by the paraboloid z= x? + y & above by the plane z=2y ?

A: The volume for the given question has been obtained in step 2.

Q: (b) Find the volume under the paraboloid z=x+y² above the triangle enclosed by the lines y=x, x=0…

A: To find the volume of the given solid.

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 solid that lies under the hyperbolic paraboloid z = 20 + x² - y? and above…

A: We have given z = 20 + x2 − y2 and R = [−2, 2] × [0, 4]

Q: What is the volume of br^3 of the region bounded by the z=9-x^2-y^2 paraboloid, the xy plane, and…

A: Triple integral is used to integrate the function of three variable over the three-dimensional…

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 enclosed by the paraboloids: z = 2x² + y? and z = 27 – x2 – 2y². %3D |

A: The given equation of the paraboloids are: z=2x2+y2 and z=27-x2-2y2 Find the volume of the solid…

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: 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:

Q: Show that the volume of the region bonded by the cone z=/x +y and the paraboloid z x+y is a/6.

A:

Q: Find the volume of the solid bounded by the paraboloids z = x? + y? and z = 2 – x² – y?. %3D %3D -

A: Consider the solid S bounded by the paraboloids z=x2+y2 and z=2-x2-y2. Find the volume of S.

Q: 6. Compute the volume of the solid that lies above the paraboloid z = r² + y? and below the…

A: Given: z=x2+y2z=x2+y2

Q: 2. Find the volume of the wedge cut from the 1-st octant in R³ by the surface z = 4-1 - y.

A: