Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion of the cone 25 25 O 160 341 O 800 341 TT 9 O 200 网。 O 200 34

Q: Find the volume of the solid that lies under the sphere: x2 +y? +z? -2z=0 and above the cone: z=3(x²…

A: Solid lies under the sphere x2+y2+z2-2z=0⇒x2+y2+z-12=1 and above the cone z=3x2+y2 Now z=3x2+y2 and…

Q: 3. Find the volume of the object cut from the cone z = Vx² + y² by the plane z = 1.

A: The volume of a solid can be obtained by considering a small volume element and integrating within…

Q: Find the volume of the part of the ball p < 1 that lies between the cones o = 1/4 and ø = r/3. -1+ 2…

A: We have to find the volume of the part of the ball rho&lt;=1 that lies between the cones phi = π/4…

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: Find the volume of the solid bounded below by the circular cone z = 2,/x² + y and above by the…

A: According to the given information, it is required to find the volume of the solid bounded below by…

Q: Evaluate the double integral V1 + 4x² + 4y²dA, where D is the region inside the circle x + y? = 25…

A: We have to find area of the region bounded by the circle given in the first quadrant of the plane.

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

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Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x? + y2 =…

A: Consider the formula for the Surface and the function f(x,y).Calculate fx and fy by partially…

Q: Consider the parallelepiped with adjacent edges u = 5i + 2j + k v = i+j+ 7k w = i + 8j + 2k %| Find…

A: The volume of the parallelepiped is 253

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Q: Find the uolume Ihe solid obtoined by rotatting the region enclosed by y= obout The line y-l

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Q: Find the surface area of the portion of the cone z=ax +y within the cylinder x+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: Calculate the surface area of the portion of the cone that lies between z=3 and z = 5. 25 25 80 OA.…

A: Equation of cone, x225 + y225 = z29therefore,z = 35x2 + y2          .....(1)

Q: Compute the surface area of the domed structure D:= {(x, y, 2) ; x² + y² + (z – 1)² = 2 ; z > 0}.

A: x2 + y2 + (z-1)2 = 2  ,  x2 + y2 + (z-1)2 = 2  ,  z ≥ 0 This equation is for sphere of radius  = 2…

Q: Calculate the area of the surface S. x2 that lies between z = 2 and z 6. S is the portion of the…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: Plot the surface z = x+y with a finer mesh (of 0.25 units in each direction),using [x,y] = meshgrid…

A: MATLAB is a computer language that engineers and scientists use to study and build systems and…

Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

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Q: Use​ Pappus's theorem for surface area and the fact that the surface area of a sphere of radius a is…

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Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x + y2 =…

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Q: Find the volume of the region bounded below by the surface z = Vx2 + y² and bounded above by the…

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

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Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: Find the surface area of the planez= x +y?from z=4 to z=9?

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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: Find the surface area of r

A: In this question, the concept of the surface area of revolution is applied. The surface area of the…

Q: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: ate the surface inte S, where S is the (x³/2 < x <1 and 0 < ce z = 3 се z (x3/2 + y

A: We have to choose the correct answer from the given options according to the given condition

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

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Q: Find the surface area generated by rotating the portion of the curve x-y = 0 from x 0 to x = 2 about…

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Q: Let S be the surface given by the first octant part of the paraboloid z=4-x^2-y^2. Find the area of…

A: We need to determine the surface area of the surface bounded by the paraboloid: z=4-x2-y2 in the…

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

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Q: Find the area of the surface. The part of the surface z = xy that lies within the cylinder x² + y? =…

A: Given Surface area (S) is Region is In polar coordinates

Q: Find the surface area of the cone z = ' + y² that lies between the plane y = x and the cylinder y =…

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Q: What is the area of the region that lies inside the circle r + y y? = 5x? ² ? %3D 10.r and outside…

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Q: nd the surface area of the portion of the cone z = Vr² + y² in between the planes z = 3 and z = 4.

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Q: Find the surface area of the portion S of the cone z2 = x? + y², where z > 0, contained within the…

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Q: The curre y=J36 - z' , -4£ x s4 will be rotated about the ルーaXis. find the area that results af the…

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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: 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: Evaluate ||x'dydz + x ydzdx + x*zdxdy over the surface bounded by z= 0 ,z %3D = h, x² + y? = a² %3D

A: here F=x3 , x2y, x2zby divergence theorem ∫∫sF.ds  =∬∫E divF dvhere S is surface bounded by  0 , z=h…

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

A: Consider the formula for the surface area.Find Zx and Zy by partial differentiation .

Q: Find the area of the surface for the portion of the sphere x+y² +z* = 225 inside the cylinder x+y…

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Q: Let be s a surface compaund by the union of s, qnd Sz An expression to get the Area of the Surface…

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Q: Find the surface area of the portion of the cone z = x2 + y2 in between the planes z = 3 and z = 4.

A: The area of the surface z=fx,y above a region R of the xy-plane is given as follows.…

Q: 4. Find the volume of the region E = { (x, y, z) ; x2 + y? + 22 Va2 + y?} Hint: The surface x2 + y?…

A: Volume of the given solid which bounded by the two given curve:

Q: Find the area of the part of the cone S = {(x, y, 2); z = Vx² + y?, x²+y² < 1}.

A: Given surface is S=x,y,z:z=x2+y2,x2+y2≤1 We have to find the area of the surface. Here, z=x2+y2…