Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25 with the largest z-coordinate. 3 (х, у, 2) %

Q: Find the center and radius of the sphere x? – 6x – 8 + y? + 4y +z? – 20z = 0 OA C(3,-2,10), r = 11…

A: Recall: Equation of the sphere :         x-a2+(y-b)2+(z-c)2=r2; where a,b,c is the center and 'r' is…

Q: Find the area of the surface. The portion of the sphere x2 + y2 + z² = 289 inside the cylinder x2 +…

A: Given equation of sphere x2+y2+z2=289 and equation of cylinder x2+y2=225

Q: The distance between the centers-of the following two spheres: x²-22x+y2-58y+z?=-961,…

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Q: Evaluate | x? zdS, where S is the part of the plane z = 2 + 4x + y above the rectangle [0, 4] × [0,…

A: To evaluate: ∫∫Sx2z dS where S is the part of the plane z=2+4x+yabove the rectangle region…

Q: Find the center and radius of the sphere x? - 10x – 10 +y? + 14y + z² – &z = 0 O A C (5,7, -4), r =…

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Q: Q2. Find the volume of the sphere x² + y +z = a (In Cartesian coordinate system). %3D

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Q: Find the center and radius of the sphere x? – 4x – 1+y? + 20y + z? – 8z = 0 O A C (2,10, -4),r = 11…

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Q: Find the area of part of sphere x² + y? + z² = 100 that lies inside x2 + y? = 10x %3D %3D

A: This is a problem of surface integral.

Q: Find the surface area of the part of the sphere x2+y2+z2=49 that lies above the cone z=(x2+y2)1/2

A: Consider the provided question,

Q: Find the area of the part of the sphere x2 + y2 + z2 = 4z that lies inside the paraboloid z = x2 +…

A: Given, x2+y2+z2=4z  and  z=x2+y2 Equation of the sphere and paraboloid in cylindrical coordinates is…

Q: Evaluate (x2 + y? + z)dS, where S is the portion of the plane z = x + 2 that lies inside the…

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Q: • Find the area of the portion of the Sphere x² + y² + 2²² = 9 between the planes Z=1 and 2 = 0.…

A: The given equation of  plane is x2+y2+z2=9. The polar coordinates are x=rcosθ & y=rsinθ. The…

Q: Find the center C and the radius r of the sphere S :x2 +y? + z2 - 2x 4y + 4z = 16 O C (2, 4, -4) and…

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Q: Find the point on the sphere x +y +z = 4 that is close O A. V11 V11 9. V11 (유 O B. 11 V11 V11

A: Solution of the problem as follows

Q: Find the volumes of the regions

A: The Volume of  the wedge, where D is the solid and R is the region, is calculated as,…

Q: Find the points on the sphere x² + y° + z?=1. that are closest to and farthest from the point (2, 1,…

A: Given, x2+y2+z2=1   ;   point (2,1,2)

Q: Find the area of the surface. The part of the sphere x2 + y2 + z2 = 16 that lies above the plane z =…

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Q: Find the radius of the sphere x2 + y? + z? – 2x – 8 = 0. %3D 4 O 2 O 3 9,

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Q: Find the surface area of the portion of the sphere x2 + y2 + z2 = 25 inside the cylinder x2 + y2 =…

A: Recall:  The formula of surface area is S=∫∫S1+∂z∂x2+∂z∂y2 dA

Q: Find the area of the surface. The portion of the sphere  x2 + y2 + z2 = 100  inside the cylinder…

A: To find the area of surface

Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 81 that lies above the plane z =…

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Q: Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }

A: Given integral is ∭x2+y2+z2xyzdxdydz over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 } Change…

Q: 10. Find the area of the portion of the sphere x2 + y² + z² = 16 between the planes %3D z=1, z=2.

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Q: The solid enclosed by the sphere x² +y² +z? = 4a* and the planes z = O and z = a.

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Q: The portion of the sphere x² + y² + z² = 25 inside the cylinder x2 + y² = 9

A: Given: The portion of the sphere x2+y2+z2=25inside the cylinder x2+y2=9 To find the area of the…

Q: c) [. The intersection of the sphere B and the xz-plane is (x - 2)² + (z + 1)² 2)² + (z + 1)² = 9.…

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Q: 8. Find the surface area of the part of the sphere x2 + y? + 22 : = 4z that lies inside the…

A: The solution is given as

Q: Find the area of the part of the sphere x2+y2+z23D 9z that lies inside the paraboloid z =r+y?. a.…

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Q: The part of the sphere x? + y? + z? = 16that lies between the planes z = -2 and z = 2. (Enter your…

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Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

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Q: Describe the intersection of the horizontal plane z = h and thehyperboloid −x 2− 4y 2 + 4z 2 = 1.…

A: Put z=h in given equation -x2-4y2+4h2=1⇒x2+4y2-4h2=-1

Q: Find the area of the part of the sphere x2 + y? + z² = 4z that lies inside the paraboloid z = x2 +…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 49 that lies above the plane z =…

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Q: Find the volume of the sphere x? + y² + z² = a² (In Cartesian coordinate system).

A: To calculate the volume of the sphere, use the following formulae.…

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 2z2 = r? + y? and…

A: Let's find.

Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 5x +y+Z = 10 is ? O A.…

A: The volume of the tetrahedron enclosed by the coordinate plane 5x+y+z=10   …..(1) is will be given…

Q: Find the area of the cap of the sphere x2 + y² + z? = 2 cut by the cone z = Vx2 + y² |3D

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Q: + + Find the area of the portion of Sphere x² + y² + 2 = 9 betw= the planes Z=1 and 2 = 0. Draw

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Q: )الكــره the Sphere OThe Portion of planes z=l x +y+Z² = \6 between the %3D and z=2.

A: Volume of the sphere x2+y2+z2=16 or x2+y2=16-z2 is: V=∫z=12∬x2+y2≤16-z2dxdydz   =∫z=12π16-z2dz…

Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: Find the area of the portion of the sphere x2 + y² + inder x2 + y? = 6y. %3D

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Q: 8. Draw the figure and Find the area of the part of the sphere x? + y? + z? = 3z that lies inside…

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Q: Evaluate [[[(x + y² +=?)? dV, where 2 is the solid hemisphere (half of the sphere) enclosed by x? +…

A: Solved below...

Q: Find the area of the surface. 12. The part of the sphere x2 + y2 + z2 = 4z that lies inside the…

A: Solution:GivenSphere:   x2+y2+z2=4zParaboloid: z=x2+y2To find the area of the…

Q: Consider the sphere (x−3)2+(y−2)2+(z+1)2=32(x−3)2+(y−2)2+(z+1)2=32. The point P =(−1,2,3)(−1,2,3) is…

A: Given that, x-32+y-22+z+12=32 And the point on the sphere is p-1,2,3 To find another point on the…

Q: Find the distance between the spheres x2 + y? + 22 = 4 and x2 + y + z = 4x + 4y+4z- 11. %3D Answer +…

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Q: Find the area of the surface. The part of the sphere x2 + y2 + z² = 36 that lies above the plane z =…

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Q: Find the area of the surface. The portion of the sphere x2 + y² + z² = 625 inside the cylinder x2 +…

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Q: Find the surface area of a quarter of the sphere x? + y2 + z2 = 4.

A: The equation of a sphere centered at x0, y0, z0 is defined using the formula: x-x02+y-y02+z-z02=r2,…