6l@) n spnenical oordinates (p,O,Ø), the equation Ô = C where C s a constert repretents in eg. á line, a plane, Q cone... A let E be the ball of radius 3 centred Qt the C6) onigin In spheni cal wordinares , Yhe integral SST. zdzdydz becomes..

Q: 1. Let S be the part of the cone z? = x? +y² that lies between the planes z = 1 and z = 2. Compute…

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Q: 7.H Jse the divergence theorem to evaluate where S is the sphere x+y? +? = 4 oriented with outward…

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Q: Evaluate the surface integral ff, z ds, where S is the portion of the graph of x = 1- z? cut by the…

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Q: Find the surface area of the region formed by the portion af the plane y+z= 10 inside the cylinder +…

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Q: Let S, be the part of the paraboloid z = æ² + y² that is inside the cylinder a? + y² = 1,S2 the part…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the volume of the solid bounded by the paraboloid z= 20 - 5x? - 5y and the plane z = 15 V =…

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Q: Evaluate || zdS, where S is the surface whose: S Sides S1 are given by the cylinder x? + y? = 1,…

A: It is given that: Side S1 are given by the cylinder x2+y2=1 Bottom S2 is the disk x2+y2≤1 in the…

Q: Let B be the sphere x2 + y? + z2 = 1. %3D The volume of the portion of B contained in the first…

A: x2+y2+z2=1

Q: 4. Let S be the surface of the solid region in the first octant bounded be- tween the spheres a2 +…

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Q: Using the spherical coordinate evaluate a) , x? dv, where G is a solid region between the sphere x?…

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Q: Q19// If F = yi +j- xk , Evaluate , F dv where V is region bounded by the plane z-0 and the surface…

A: 19Given that:¯The vector field is F→=yi^+j^-xk^ and the region R is boundedby the plane z=0 and the…

Q: Let S, be the part of the paraboloid z = 2? + y? that is inside the cylinder a? + y? = 1, S2, the…

A: Given S1 be the part of the paraboloid z=x2+y2 that is inside the cylinder x2+y2=1. we have to find…

Q: The portion of the surface h x² + y? with h, a > 0, 2 = -. a between the ry-plane and the plane z =…

A: Given that:   The portion of the surface is given as: z=hax2+y2  with h,a>0

Q: Find the lateral surface area of the part of the cylinder a + y = 1 that lies within the sphere z²…

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Q: Calculate /| xz dS, where K is the part of the cone z = Va2 + y? where z < 2.

A: Given the surface

Q: Let D be the region in space lying inside the sphere 2² + y² + z? = 4, outside the cone 22 = 3(2 +…

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

Q: Compute the surface area of the portion of the sphere with center the origin and radius 4 that lies…

A: We have to compute the surface area of the portion of the sphere with center the origin and radius 4…

Q: Using Green's formula, calculate the line integral fordz + (z + y)*dy, where the contour C is the…

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Q: Calculate the area of the surface S. S is the lower portion of the sphere x + y 2 + z2 = 49 cut by…

A: Answer : The surface area of sphere cut by cone is in following pic :

Q: Find the area of the portion, for which z > , of the sphere in R with radius v3 centered at the…

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Q: I the volume of the solid cut from the cylinder a? + y? = 16 by the planes z = 0 and æ + kçe: z² +…

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Q: Consider the parallelepiped with adjacent edges Find the volume. V = i u = Si + 5j + k v = i + j +…

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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: The volume of the solid that lies above the cone z = V3/x2 + y? and below the sphere z = x? +y? + z2…

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Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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Q: Find the volume of the solid inside the sphere p = 4 that is bounded above by the cone = T/3 and…

A: According to question, ρ = 4,ϕ = π3

Q: If E is the region inside the sphere r2 + y? + z² = 4, below the cone z = /3x² + 3y², above z = gral…

A: Given If E is the region inside the sphere x² + y² + z² = 4, then the integral in spherical…

Q: Evaluate F. dS, S where F(x, y, z) = (3xz – Vy? + 2?, sin(x – 2), e" - z²) and S is the surface…

A: Since S is the boundary of closed region in space. So we apply the Gauss Divergence Theorem.

Q: 1. Consider the surface which is the part of the sphere r? + y? + 2? = 4 that lies above the cone z…

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Q: Consider the parallelepiped with adjacent edges u = 3i + 8j + k v = i + j + 8k w = i + 6j + 6k Find…

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Q: ind the volume of the solid cut from the cylinder x2 + y² = 36 by the planes z = ürkçe: a² +y²…

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Q: Consider the ray r(t)=o+ td with origin o=(1, 1, 0) and direction d = (1, 1, 1), and the plane N-x=…

A: To find the point of intersection of the ray and the plane. Given: equation of ray is: r(t)=o+td…

Q: (b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz,…

A: Stokes theorem  ∮CF.dr=∫∫SCurl F .dS Where S be a smooth surface that is bounded by a  closed,…

Q: SSS, xz dV, where D is the solid region in the first octant bounded above by the sphere x + y2 + z?…

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Q: The volume of the solid that lies above the cone z = v3/x² + y? and below the sphere z = x? + y² +…

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Q: Let B be the sphere x? + y + z? = 4. The volume of the portion of B contained in the first octant is…

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Q: 6. Evaluate the surface integral where o is the portion of the cone z = Vr? + y? between the planes…

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Q: Consider the parallelepiped with adjacent edges u = 3i + 2j +k v = i+j+4k w =i+6j + 2k Find the…

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Q: 9. Find the volume of the solid enclosed by the cone z = Vx? + y? and the plane z = 4.

A: we have to find the volume of the solid

Q: The contour of integral zdz z dz of the cirle z-i =2is 8 TAO 8 Ti B O -8 TticO

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Q: Find. Hhe volume,Ť the selis by I Hhe revolutinn for fa)='4- E[0, about XE [0,1] %3D usin the disk…

A: Since, you have asked multiple question, as per our company guidelines, we will solve the first…

Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

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Q: Let T be the triangle in the xy plane enclosed by the line y = 22 x and the -axis between x = 0 an x…

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Q: 2. Let G be the region in R that lies inside the cylinder r? + y? = 4, above the ry plane, and below…

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Q: Find the surface area of a) The part of the plane 3x + 2y +z = 6 that lies in the first octant b)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Find the Surface area A= SSirlpde f te pertien of she sphere of radins y that les intide the inder…

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Q: Let S be the sphere x + y² + z? = 9 oriented outwards, and F = (5x, 7z, –3y). Evaluate: F. dS. The…

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Q: Let D be the annulus 1<x2 + y² < 9, and let Ca denote the circle of radius a centered at the origin…

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