Find the positive constant A given that the volume of the solid bounded by the paraboloid, x2 + y2 +z = A  in the first octant is 32π .

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 z = x² + 3y² and above the region D =…

A:

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 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: Find the volume of the region bound-ed below by the paraboloid z = x2 + y2, laterally by the…

A:

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: Find the volume of the solid E whose boundaries are given coordinates. E is located inside the…

A:

Q: The volume of the solid generated by revolving the region bounded by x+ 2y =2, y=0, and x-0, about…

A:

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: Find the volume of the given solid. Under the plane 7x + 2y − z = 0 and above the region enclosed…

A: Given the plane 7x+2y-z=0 and the regio enclosed by the parabolas y=x2 and x=y2

Q: Using a triple integral to find the volume of the solid within the cylinder x^2+y^2=16 and between…

A:

Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the disk method to determine the volume of solid obtained by…

A:

Q: Given the volume R of the solid bounded by the graphs of z = 9- y², x +z = 9, x = 0 and N=0. a)…

A: Volume by triple integral

Q: The solid E bounded by z 1-x and situated in the first octant is given in the following figure. Find…

A: We calculate volume by triple integral of Cartesian coordinate

Q: Find the volume of the given solid. Under the plane 7x + 2y -z = 0 and above the region enclosed by…

A:

Q: Find the volume V of the solid below the paraboloid z= 4-x-y and above the following region.…

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

Q: Find the volume of the solid bounded by z= - y, the xy-plane, and r=4 cos 0.

A: The answer is 8.33

Q: Given that a solid D is bounded by the planes y = 10, z = 5 – 10x and coordinate planes in the first…

A: This question is related to calculation of volume of a three dimensional solid, we will use use…

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: Use a triple integral to find the volume of the given solid. The solid enclosed by the paraboloids…

A: Given paraboloids : y=x2+z2y=32-x2-z2 Taking intersection of the paraboloids

Q: Find the volume V of the solid below the paraboloid z = 4-x² - y² and above the following region. R=…

A:

Q: Using a triple integral to find the volume of the solid within the cylinder x2+y2=25 and between the…

A: we first identify which plane is above and which is below while intersecting the cylinder x2+y2=25…

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: S[(4-x-2y)dxdy 00

A: We have to evaluate the integral…

Q: Evaluate the integral [[[var !!! y² dv where G is the solid in the first octant that lies below the…

A:

Q: Use a triple integral to find the volume of the given solid. The solid enclosed by the paraboloids y…

A: Consider y=x2+z2 and y=72-x2-z2      ..... (1) Find the point of intersection…

Q: Let C denote the solid that is = 0, • bounded above by z = e-2(x² +y² ), and • lying within the…

A: To find the volume of the solid that is bounded by the below surfaces. z=e−2x2+y2 z=0 x2+y2=4

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: Find the volume of the given solid. Under the plane 7x + 2y - z = 0 and above the region enclosed by…

A: The solution are next step

Q: Use a triple integral to find the volume of the solid below the paraboloid z = x² + y² and above the…

A: Solution

Q: 5. a) Find the volume of the solid bounded by the paraboloid z= 2(x? + y²) +3 and the cylinder x? +…

A: (a)  Find the volume of the solid bounded by the paraboloid z=2x2+y2+3 and the cylinder x2+y2=1 and…

Q: Use the disk method to find the volume of the solid of revolution bounded by the x-axis and the…

A: We first graph the function using a graphing calculator

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

A: Since you have posted multiple questions according to company rule we are supposed to give solution…

Q: Find the volume of the solid under the paraboloid z=x2+y2 and above the disk x2+y2≤16.

A: Given: Paraboloid:  z = x2+y2 Disk:  x2+y2≤16 To find: Volume of the solid under the paraboloid z…

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: Find the volume V of the solid below the paraboloid z = 6-x -y and above the following region.

A: We have to calculate ∬Rz dxdy

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: Find the positive constant A given that the volume of the solid bounded by the paraboloid, x2 + y2…

A:

Q: B) Find the volume of the solid bounded by the cylinders r = y, z = y² and the planes, x = 0 and z =…

A:

Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

A:

Q: x² + y? + z² = 6z TT

A: To convert the variables x, y and z to the spherical coordinates, substitute x=ρcosθsinϕ,…

Q: Find the constant k > 0 such that the volume of the region lying inside the sphere x2 + y2 + z2 = a2…

A: Given that,k&gt;0 is a constant such that the volume of the region lying inside thesphere…

Q: Find the volume of the solid above the xy-plane, within the cylinder x² + y? = 1, and below the…

A: using cylinderical coordinates

Q: Find the volume of the solid that lies under the paraboloid z = x² + y? and above the region D in…

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: 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: Let D be the solid whose base lies on the xy plane and is bounded by the graphs of y = 2x and y = 3…

A: To find the point where the two functions intersect, equate the two.   Cross-sectional area of the…

Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

A: Introduction: A solid of revolution is a solid figure created by rotating a plane curve around a…

Q: Find the volume of the given solid. Under the plane 3x + 2y – z = 0 and above the region enclosed by…

A: