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

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: What is the volume of the solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y…

A: Given,  The solid enclosed by the planes z = 3 and x + y − z = −13, and the curves y = x2 and x = y2

Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

A: 25.   Given that:   The plane y+z=2 and the cylinder x=4-y^2. The region in the first octant bounded…

Q: Find the volume of material cut from the solid sphere r2 + z2 &lt;=9 by the cylinder r = 3 sin u.

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Q: b) Find the volume of the solid enclosed between the cone z = hr² and the plane z = 2h.

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Q: - Find the volume of the region cut from cylindrical (x² + y² = 16) by the plane z 0 and the plane…

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Q: Find the area of the surface. The portion of the cone z = 4V+ y² inside the cylinder x? +y² = 16

A: Consider the provided cone z=4x2+y2 inside the cylinder x2+y2=16. Find the area of the surface. The…

Q: Find the volume of the solid above the cone z2= 3(x2 + y2 ), z ≥ 0 and below the sphere x2+ y2+ z2 =…

A: We convert the units in spherical coordinate. The cone is given as,  The sphere is given as, The…

Q: Find the surface area of the portion S of the cone z^2=x^2+y^2 where z≥0z≥0, contained within the…

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Q: Find the Volume cutoff from the cylinder x2 +y2 = 9 by the planes z = 0 and z = 5.

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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 volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a…

A: Given :             r =2a cosθϕ=α0 &lt; α &lt;π2  To Find : Volume of the bounded region

Q: By integrating all three surface elements of a cylinder, find the surface area of a cylindrical pie:…

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Q: integrate ƒ over the given region. ƒ(u, y) = y - sqrt(u) over the triangular region cut from the…

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Q: Given the area bounded by the curve y^2 = 4x and y^2 = 8x − 8. Determine the centroid area bounded…

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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: Miscellaneous volumes Use a triple integral to compute thevolume of the following regions.

A: The given equation of cone is and plane is, z=1-x2+y2 x+y+z=1

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

A: Let z=f(x,y) is differential over the region R. Then surface area is A=∫∫R1+fx2(x,y)+fy2(x,y)dydx

Q: Find the surface area of the portion of the surface x2- 2 In a+ V15 y - z = 0 above the rectangle 1…

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Q: . Find the area of the surface obtained by rotating y = S, Vs² – 1 ds, 1 < x < 2 about the y-axis.

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Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: Find the volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a…

A: Given: the sphere r=2a cos theta , cone ϕ=α0&lt;α&lt;π2

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

A: Given the surface

Q: (c) By using double integrals, find the surface area of plane 2x + 5y + z = 10 that lies inside the…

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Q: Find the uolume of the region abave the メy- plane inside the cone xZ+y2 glirder and inside the…

A: Convert the parametric form.

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: Find the volume of the solid that lies within the sphere x² + y + z² = 81, above the xy plane, and…

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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: Find the area of the section of the surface x = u2, y = uv, z = v2/2 bounded by the curves u = 0, u…

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Q: Solve for the area of the portion of the cylinder x = V1 – y², which lies between the planes z = 0…

A: Line integral

Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

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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 x+y+z= 6 plane part remaining in cylinder x2 + y2 = 6

A: The area of the plane, z=f(x,y) remaining in a surface is calculated by the formula below .…

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: Find the average value of the square of the distance from the point P(x, y) in the disk x2 + y2 ≤ 1…

A: Calculate the distance D between point P(x,y) to point A (1,0). D=(1-x)2+0-y2D=1-x2+y2 Calculate…

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

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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: Find the area of the surface given by f(x, y) = 8 + 4x – 5y that lies above the region R= {(x, y) :…

A: The surface f(x,y)=8+4x-5y that lies above the region R=x,y:x2+y2≤1.

Q: Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

A: The given plane is z=3x+5y+3. Differentiate partially with respect to x, y respectively to obtain…

Q: Find the volume of the solid that lies under the plane 4x + 10y - 2z + 15 = 0 and above the…

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

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Q: Find the volume of the solid that lies within the sphere x² + y² +2²=81, above the xy plane, and…

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Q: Find the average distance from a point P(x, y) in the disk x2 + y2&lt;=a2 to the origin.

A: Average distance is given as

Q: Find the volume of the solid enclosed by the cone z = sqrt(x2 + y2) between the planes z = 1 and z =…

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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: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.

Q: Find the volume of the solid that lies under the double cone z2 = 4x2 + 4y2, inside the cylinder x2…

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