2. Find the volume of the solid lying under the elliptic x2 paraboloid + 4 y2 +z = 1 and above the rectangle 9 R = [0, 4] × [-1, 4].

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 hyperbolic paraboloid z = 3y² – x² + 2 and above…

A:

Q: Find the volume of the solid bounded by the - 3+ 2x2 + 2y? and paraboloids z = z = 5 – x2 – y? -

A: To find the volume of the solid bounded by, z=-3+2x2+2y2 and z=5-x2-y2

Q: 5. Find the volume of the tetrahedron bounded by the coordinate planes and the plane 3x + 6y + 4z -…

A:

Q: 2) Find the volume of the solid bounded by the cylinder x2 + y = 16 and from z = 1 to z + x %3D 2…

A:

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

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 solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 2 and above…

A: Given:z=3y2-x2+2 above the rectangle R=-1,1×1,5Formula:V=∬R z dx dy

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

A:

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

A:

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

A:

Q: Find the volume of the solid under the paraboloid z = 4–x²–y² and over the region x²+y² < 1.

A: We have to find the volume of the solid.

Q: Find the volume of the solid enclosed by the paraboloids z = 1 (x2 + y²) and z 32 – 1 (x2 + y²).

A:

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: 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 enclosed between the paraboloids z = z = 6 – 2.x2 – y². x² + y? and -

A:

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

A:

Q: Find the volume of the solid below the paraboloid 1 =(9-x2-y²), above the xy-plane and outside %3D…

A:

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

A:

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

A:

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

A:

Q: Estimate the volume of the salid that lies alove the square R-[0,2] [0,2] and below the eliptic…

A: The region R can be divided into four equal squares as follows: Note the upper right corner points…

Q: 4. Find the volume of the solid that lies within both the cylinder a²+y² = 1 and the sphere a2+y² +…

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: 5. Find the volume under the paraboloid z = -x² – y², and above the cone z = -. -V#²+ y².

A: Given

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 solid bounded by the paraboloids z = – 5+ x? + y? and z = 6 – 2x? – 2y? -

A:

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

A:

Q: Find the volume of the solid bounded by the paraboloid z = 16 – x2 – y?, the cylinder x2 + y? = 8…

A:

Q: - Find the volume of the solid that is bounded above by the cylinder z = 4-x2, on the sides by the…

A:

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: Find the volume of the solid that lies under the elliptic paraboloid z = y^2 + 8x^2 + 1 and above…

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: 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: Define R as the region bounded by the graphs of f(x)=4x2 −4x+2, x=0, x=1, and the x-axis. Using the…

A: We have to find volume of solid of revolution about x axis .F(x) and graph  is given below :

Q: Find the volume of the solid that lies under the plane 4x + 10y - 2z + 15 = 0 and above the…

A:

Q: 1. Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x =…

A: Note: Hi! Thank you for the question As per the honour code, We’ll answer the first question since…

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: Calculate the volume under the elliptic paraboloid z=x^2+3y^2 and over the rectangle R=[−4,4]×[−2,2

A:

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: Find the volume of the given solid. Enclosed by the paraboloid z = 5x2 + 2y2 and the planes x = 0, y…

A: We have to find volume of paraboloid.

Q: Define R as the region bounded by the graphs of f(x)=x2 +4x+5, x=−3, x=0, and the x-axis. Using the…

A: Please see the diagram on the white board. The line in blue is the plot of the given curve f(x)=x2…

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

A: Given: To Find: The volume of the region bounded above by z=3-x2-y2 and below by z=2x2+2y2.…

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

A: