Let Sj be the closed surface consisting of S in Figure with the unit disk. Find the volume enclosed by S1, assuming that together II (x. 2y, 3z) · d$ = 72 Unit circle FIGURE Surface S whose boundary is the unit circle.

Q: Find the area of the portion, for which z > T9, of the sphere in R° with radius /3 centered 2 at the…

A: Here we find the area.

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: Find the volume under the paraboloid z-x+y above the triangle enclosed by the lines y=x, x=0 and…

A: Volume is the amount of space occupied by the closed surface. In this problem, we have to calculate…

Q: and stra ight and x:8 Let R be an area enclosed by a curve. : 1 Using the disc method, which is the…

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Q: Find the volume under the surface formed by f(x, y) = xy2 over the rectangle %3D 0 Sa<2 and 0 SyS 3.…

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Q: Find the volume of the prism whase base is the triangle in te Xy-plane bonnded by the x - axis and…

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Q: Find the surface area of the sphere with radius of 7 in. Leave your answer in terms of T. 287 in 2…

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Q: Evaluate the volume between the surfac x²y, and the rectangle in the xy 2 = plane given by 2 < x <…

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Q: Set up, but do not evaluate, an iterated integral that equals the surface integral |/ (2² – y²) dS,…

A: Given data:   The given surface integral is I=∫∫S(z2-y2)dS. The given part of the cone is…

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: FR,y-I, and x= | , a bout

A: Given that,

Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

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Q: Use the Divergence Theorem to evaluate F. ds, where F(x, y, z) = z?xi + (+ tan zj + (x²z + y2)k and…

A: We are given a closed surface integral and we have to use the Divergence Theorem to evaluate that.

Q: Let R be the rectangular region R: [0,8]x[0,1] in the xy-plane. By identifying it as volume of a…

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Q: Set up, but do not evaluate, an iterated integral that equals the surface integral || F · dš, where…

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Q: If E is the region inside the sphere x2+y?+z² = 4, below the 3x2 +3y? and y 2 0, then the integral…

A: Use the following formulae which gives the relation between the spherical coordinates and the…

Q: If R is the region bounded by y = r2-1 and y = -r- 1, find the volume V(S) of the solid S generated…

A: Given that, R is the region bounded by y=x2-1 and y=-x-1.

Q: Identify the theorem: If S is the boundary surface of a solid E in 3-dimensional space, then SS, F.…

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Q: Use polar co ordinates to find the volume of the given solid  above the cone z=sqrt{x^2+y^2} and…

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Q: Use the Theorem of Pappus and the fact that the volume ofa sphere of radius r  is 4/3πr3  to find…

A: We have, The volume of a sphere is V=43πr3                               ⋯⋯1. The semi-circular…

Q: Find the volume V inside both the sphere x² + y² +z² = 1 and the cone z = V/x² + y².

A: Use the conversion formulas to write the equations of the sphere and cone in spherical coordinates.…

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: Let F=[x+y, y+z, x+z] and S be a sphere of radius R. Using the divergence theorem, the value of the…

A: Topic- vectors

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: The volume of the solid bound by the two surfaces is z = 8- 3(x² +y?), z= (x² + y?)² - 2.

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Q: Let o be the portion of the plane x + y = 1 that is in the first quadrant and is between the…

A: Let be  the portion of the plane x+y  = 1 that is in the first quadrant and is between the…

Q: Consider the paraboloid z = 1- ² – y?. Find the volume of the region between this surface and the ry…

A: According to the problem,. we have

Q: 4. For r > 0 and h > 0, show that the conical set S = (x, y, z) | x > 0, y > 0, z > 0, z2 h?(r2 - x²…

A: Given that the surface S is S=x,y,z|x&gt;0,y&gt;0,z&gt;0, h2=h2r2-x2-y2 We have to find the surface…

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: Let o be the surface of the sphere given by r? + y? + z² = a². Evaluate the surface integral f,(x² +…

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Q: Use the Divergence Theorem to evaluate [, F• dS, where F(x, y, z) = z²x i + (y + tanz)j + (x²z +…

A: We will find out the required value.

Q: Determine the volume of the region that lies under the sphere x² + y² + z² = 4, above the plane z…

A: Given: Now,

Q: Let C be the portion of the circle x² + y² = 4 from (2,0) to (0,2) traced counterclockwise. (a) (b)…

A: As per the question we are given a curve C which is a quarter circle defined as : x2 + y2 = 4  ,…

Q: ordinates to find the volume

A: Given surface: z=e-x2-y2-e-9 and XY plane To find: Using polar coordinates, find the volume of the…

Q: Find the area of the surface given by r(u, v)=9ui-vj+vk, where 0≤u ≤2 and 0 ≤ y ≤4. O 45√2 O 38/2 O…

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Q: Let o be the surface of the sphere given by r² + y? + z² = a². Evaluate the surface integral [S,(r²…

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Q: If E is the region inside the sphere x2 + y² + z² = 4, below the cone z = V3x2 + 32, above z = 0 and…

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Q: Evaluate the surface integral of G over the surface S. S is the hemisphere x+y+z = 12, z2 0;…

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Q: Compute the area of the part of the surface S which is the part of the plane r(u, v) = that lies…

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Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: Let A = 6 zi + (2x + y)j – x k ; Evaluate A.ndS over the entire surface S of the region bounded by…

A: Please see the figure below to comprehend what's going on:

Q: Prove the following relationships If (S) is the surface surrounding volume (t) : fodi = -[(V$)ndš s,…

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Q: The volume of the solid enclosed by the surface z = 1/y and the rectangle 2 <r<4, 1<y<e in the…

A: We use double integral to find the volume of the solid.

Q: use the Causs theorem to reduce the surface integral (JA.ds) on all six faces of a cube whose volume…

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Q: Evaluate the surface integral of g(x,y.z) = z over the surface S, where S is the hemisphere x +y +z…

A: Detailed solution is given below.

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

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Q: Refer to the figure and find the volume V generated by rotating the given region about the specified…

A: To compute the volume of the required solid of revolution

Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: We know by the theorem of Pappu that the volume of a solid is obtained by area times the distance…