Find the area of the part of the plane x + 4, y + z = 4 that lies in the first octant. 1. A = 12 2. A = 6V2

Q: Evaluate y*dz – r*dy, where C is the boundary of the region between the circles r? + y? = 4 and z² +…

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Q: 3. Find the volume of the tetrahedron in the first octant that is bounded by the three coordinate…

A: Given the equation of the plane, z=5-2x-y  ⋯⋯(1) Rewriting equation (1), 2x+y+z=5  ⋯⋯(2) At z=0,…

Q: Calculate the surface area of the following: the cap cut from the sphere r² + y² + z² = 3 by the…

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Q: 13. The volume generated when the region bounded by the curve x = /1+ y, the y-axis and the lines y…

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Q: 25. Find the volume of the solid that is enclosed by the cone z = Vx² + y? and the sphere 22 + y? +…

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Q: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

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

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Q: Find the area of the plane x+2y+2z=2 cut out by the cylinder x^2+ y^2=4

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Q: answering this question. Please you specify each step and for ble. ank You. me of the region between…

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Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

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Q: f(x, y) = xy, R = {(x, y): x² + y² < 16}

A: Polar coordinate and rectangular co-ordinate  x=r cosθy=r sinθx2+y2=r2θ=tan-1yx The integral will be…

Q: Find the area of the part of the cylinder y2 + z2 = 4 in the first octant, cut out by the planes x =…

A: Given. We are given a cylinder in the first octant.. y²+z² = 4 We need to find the volume of the…

Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

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Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

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Q: Find the volume of the solid cut from the cylinder x2 + y? = 25 by the planes z = 0 and x + z = 2.

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Q: Find the volume of the region in the first octant enclosed by the cylinder x^2 +y^2 =4 and the plane…

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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: 4. Find the exact value of surface area of the solid that is described by the intersection of the…

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Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: 2. Find the volume of the region enclosed by the paraboloid z = x2 + y? and the plane z 2x.

A: Given paraboloid, z=x2+y2and the planez=2x To find the volume of region enclosed by the paraboloid…

Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

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 olume of the solid cut Prom the sphere 8=2C@SQ by the Cone Z= Jx+ ý Ans/ T

A: The given question is related with triple integral. We have to find the volume of the solid cut from…

Q: 3. Find the volume of a solid enclosed by the parabolic cylinder y = x², the planes z = 0 and y +z =…

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Q: Find the volume of the solid cut from the cylinder x² + y? = 4 by the planes z = 0 and x +z = 6.

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Q: Find the surface area of the portion of the surface z = xy which is inside the cylinder p2 +3? = 9.

A: It is given that the portion of the surface is z=xy=fx,y. The surface area of the surface is…

Q: f (x, уy) %3D — 3х — 2у + 6 | R = {(x,y) : 0 <x< 2,0< y< 2 – x )}

A: Given query is to find the area bounded by the region.

Q: e want to compute the volume of the tetrahedron cut from the fir ane 6x + 3y + 2z = 6. Which one is…

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Q: Evaluate ||| Vx2 + y2 dV, where E is the region that lies inside the cylinder x2 + y? = 25 and…

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Q: Find the area of the surface of the part of the cylinder ? + 2² = 4 that lies above the square in…

A: For the given part of the cylinder  x2+z2 =4  which lies above the x-y plane at the vertices…

Q: 3. Find the centroid of the region bounded by the parabola y? = 4x, the y-axis, and the line y = 4.

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Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

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Q: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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Q: Find the area of the part of the plane 4x + 3y + z = 12 that lies in the first octant.

A: to find:- surface area, A.

Q: Find the area of the part of the sphere r? + y + z² = 4 that lies within the first octant and inside…

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Q: Find the approximate area of the surface obtained by rotating x = - (y° + 2)/², 1 sys2 about the…

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Q: 4 The area of the surface S = {(x, y, z) € R³ : z — 5 — z² - y², z ≥ 3} equals (A) 4T (B) (C) (D)…

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Q: Which of the following equals to the area of the plane region bounded by the ellipse 4x²+y² = 4.…

A: Here we find area for given ellipse.

Q: Find the area of the upper portion of the cylinder x² + z? = 1 that lies between the planes x = ±1/2…

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Q: Find the area of the part of the surface z = xy that lies within the cylinder x2 + y2 = 9.

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Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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Q: 7. Calculate the area of the portion of the sphere x +y +z2 = 49 between z= 2 and z=V2. 2 %3D OA.…

A: Surface area of the surface given by z=f(x,y)  A=∫∫D1+fx2+fy2dA where  D is projection of surface on…

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

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Q: Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2…

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Q: 4. Find the exact value of surface area of the solid that is described by the intersection of the…

A: For a function, z=f(x,y) the surface area is calculated using the formula below. S=∬D[fx]2+[fy]2+1dA

Q: 1) A) Find the area of the portion of the sphere x? + y + =9 lying inside the cylinder x2 + y? = 3y.

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Q: (a) Find the surface area of the plane 3x +2y + z = 6 that lies in the first octant.

A: If z=fx, y then surface area is, AS=∫∫D1+zx2+zy2dA

Q: Find the area of the part of the plane  5x + 3y + z = 15  that lies in the first octant.

A: From the given statement, the plane is 5x + 3y + z = 15 and it is lies in the first octant.

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

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