(7) Let D be the solid above the cone z = r and below the sphere of radius 2, and let fla, 4, 7) = x2 + y? + 22,

Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: A per your request , (b) The equation of sphere is given as , x2+y2+z2=Rs2 and Radius of drill=Rd…

Q: F D' Point D is the Nof AABC because AF, BG, and CE are all centroid incenter Submit Answer…

A: We know that, The circumcenter of a triangle is the point where the perpendicular bisectors of the…

Q: 6. The solid bounded by x = y², and x = 8 – 2z2 – y?.

A: To find the triple integral over the given solid bounded by x=y2,x=8-2z2-y2.

Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

A:

Q: d. .2 The solid bounded by the cylinder x+y = 9 and the planes z = 0 and z = 3- x. %3D

A: The solution of the problem is given in the next steps.

Q: 28. F(x, y, z) = x³i+y°j+z°k, and S is the sphere of radius 3 and centered at the origin.

A: divF→=ddxx3+ddyy3+ddzz3        =3x2+3y2+3z2        =3x2+y2+z2  by divergence theorem,…

Q: 39.) The solid bounded by the cylinder x+y² = 9 and the planes z= 0 and z = 3 - x. 40

A:

Q: Evaluate ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

A:

Q: 4. Find the volume V of the solid S that is bounded by the elliptic paraboloid defined by 2x2 + y2…

A:

Q: 2. The solid outside the cylinder x² + y² = 1 that is bounded above by the sphere x² + y? + x? = 8…

A: The solution is given below

Q: sketch the solid whose spherical coordi- nates (p, 4, 0) satisfy the given inequalities. 0<p<2/cos…

A:

Q: Find the extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular…

A:

Q: 5. Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 18). R h…

A:

Q: 18. The volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane z = 6

A:

Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: 2). Find the flux of F(x, y, z) = (0, yz, z) outward through the surface S cut from the cylinder y +…

A:

Q: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

Q: A: Determine the mass and center of mass of the solid that bounded by the paraboloid = 9y? + 9x2 and…

A:

Q: 2. Evaluate the triple in tegral where E is the y-2x2+2z20nd the plane y= 8. solid bounded by SI…

A:

Q: A solid G is bounded by the paraboloid z = 4 – x2 – y², the cylinder 22 + y? = 4 and the plane z =…

A:

Q: The plane z =0 separates region 1 (z 0), which is a dielectric material with ɛ, = 4, from region 2…

A: The complete solutions are given below

Q: 4. Find each volume. (a) A solid is being bounded by paraboloids z = 2x² + y? and z = 27 – x² – 2y?.…

A: We have to find the volume  from the given condition

Q: e of the solid E whose boundaries are given in rectangular located inside the circular cone x? + y?…

A: In this question we will use basic of calculus i.e volume of cone. We will simply draw the given…

Q: Considering f(, Y, z) = z + x²y and S as part of the cylinder y² + z² = 25 that is between the plans…

A: It is given that surface S is the part of the cylinder y2+z2=25 lies between the planes x = 0 and x…

Q: Find the volume of a right circular cylinder of radius a = 4.00 with a paraboloid of revolution…

A:

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: The region shown is bounded by x = 3, y = 0, and y = x. y 1 1 2 3 4 If the region is rotated about…

A:

Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

A:

Q: 3. Find the volume under the paraboloid 3z = 2.12 + 2y2, above the triangle enclosed by the lines y…

A: First we have to draw graph and find limit according to which we have taken strip along y . Find…

Q: 17 The solid bounded by the surface y =x² and the planes y+z=4 and z = 0.

A: To find the volume of the solid

Q: FD is the region in the first octant between the spheres x2+y2+z²=1 and x2+y2+z²=16, then dV =

A: Converting into spherical coordinates

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

A:

Q: Evaluate the triple integral. 4xyz dv, where Tis the solid tetrahedron with vertices (0, 0, 0), (1,…

A:

Q: a. Let S be the cylinder with base a circle of radius 2 in the xy-plane centered at (2,3,0) and with…

A: S is the cylinder with base a circle of radius 2 in the xy-plane centered at 2,3,0 and height 3…

Q: (a) Compute the area of the portion of the cone x2 + y2 = z? with z 2 0 that is inside the sphere x2…

A:

Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

A:

Q: 1) Consider the solid Q in the first octant, generat surfaces: z = (y – 3)² + 1, 2r + 4z = 16, 1= 1,…

A: Volume of solid: Let z=f(x, y) and z=g(x, y) be the functions of x and y of a solid, and let x=a to…

Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

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: 9. The solid bounded by x = 1 – y?, z = y², x = 5, and z = 9.

A:

Q: XII. $F•d$ where F = (x,y,z²) and S is sphere of radius 2 with center at 0.

A: F→=x,y,z2, surface S is sphere of radius 2 with centre O=0,0,0To find: ∯SF→.dS→

Q: 1. Compute the average height of the cone z = a> 0. r² + y² above the disk x² + y² ≤ a² for

A:

Q: O 9/ Compute I - [.lryz) , uhere s is the part g the plane y +x that lies inside the half-cylinder…

A: We know that, dS=1+∂z∂x2+∂z∂y2dydx where S is the part of plane z=y+x. ∂z∂x=1∂z∂y=1 dS=1+(1)2+(1)2…

Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

A:

Q: E) Sketch the solid bounded by the cylinder ** +y = 4 and the planes y+z = 4 and z = 0

A: Here, we need to sketch the solid bounded by the cylinder x2+y2=4 and the planes y+z=4 and z=0.

Q: 5. USC cyllndrical coordinates. Evaluatc (k4)dv, where E IS the solid that ies betwern the cylinders…

A:

Q: 15. The solid enclosed by the sphere x2+ y2 + z2 = 4a? and the planes z = 0 and z = a. %3D

A: Given: x2+y2+z2=4a2          ... (1) z=0z=a

Q: A fluid has density 600 kg/m3 and flows with velocity ū = ri + y. measured in meters, and the…

A: Here we have, Velocity v→=xi^+yj^+zk^ where x,y, and z are measured in meters.  the equation of…

Q: 1) Find the volume of the solid that lies between the paraboloid z = 2x² + 2y² and the plane Z = 8.

A: The main objective is to find the volume of solid that lies between the paraboloid z=2x2+2y2 and the…