Calculate the surface area of the following: the cap cut from the sphere r² + y² + z² = 3 by the cone z = Vx2 + y2.

Q: 3. Find the volume of the solid that lies within the sphere ++- 4 above the ry- plane,and below the…

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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: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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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: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Find the area of the surface S where S is the cap cut from the paraboloid z = 2– x – y by the cone z…

A: Given that : z=2-x2-y2z=x2+y2 Now, to find the point of intersection , 2-x2-y2=x2+y2Put…

Q: Find the surface area of the part of the sphere x2+y2+z2=49 that lies above the cone z=(x2+y2)1/2

A: Consider the provided question,

Q: Classify the quadric surface. 22 = x² + y? + 1 81 ellipsoid elliptic cone ollintio naraboloid

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Q: Let S be the part of the hyperbolic paraboloid z = x2- y2 located between the cylinders x2 + y? = 1…

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Q: Find the volume of the solid that is enclosed by the cone  z = sqrt(x2 + y2) and the sphere  x2 +…

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Q: Find the volume of the solid that lies under the elliptical paraboloid z = 2x? + y + 4 and above the…

A: V=∫∫RzdA V=∫01∫012x2+y2+4dydx Integrate with respect to y, V=∫012x2y+y33+y01dx…

Q: Compute 3xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: Evaluate ||y dS.where S is the part of the sphere x +y° +z° =1 that lies above the cone z=Vx +y

A: x2+y2+z2=1z=x2+y2Given

Q: The volume of the tetrahedron enclosed by the coordinate planes and the plane 9x +y +Z = 18 is ?

A: We want to find the volume of the tetrahedron enclosed by the co-ordinate planes, i.e. x=0, y=0, z=0…

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

A: Given

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: Find the surface area of the portion of the cone z? = 4x? + 4y? that is above the region in the…

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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 surface area of the part of the plane 2x + 5y + z = 2 that lies inside the cylinder x? +…

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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 area of the part of the sphere x2+y2+z23D 9z that lies inside the paraboloid z =r+y?. a.…

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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: 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: Find the surface area of the part of the circular paraboloid z = x + y that lies inside the cylinder…

A: Solve the given

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: Show that the volume of the region bonded by the cone z = Vx² +y2 and the paraboloid z =x² +y is…

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Q: Find the surface area for the portion of the hemisphere z =sqrt(4 − x^2 − y^2) that sits above the…

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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 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: Find the area of the cap of the sphere x2 + y² + z? = 2 cut by the cone z = Vx2 + y² |3D

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Q: Calculate the surface area of the paraboloid with top radius R> 0 defined by 2 a² + y? 0< x² + y? <…

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Q: Use the change of variables formula to prove that the volume of the ellipsoid given by ()* + (#)* +…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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: 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 surface area of the part of the sphere x2+y2+z2=9 that lies above the cone z=√x2+y2

A: answer is below

Q: y e 3x, x 2 0, is rotated about the x-axis, find the area of the resulting surface. If the infinite…

A: Find the area of the curve when rotated about x-axis

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

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Q: Find the surface area of a sphere of radius r

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Q: Find the surface area of the paraboloid z = x² + y², 0 < z < 1. .

A: The surface is same as revolving the curve x2=z or x=z1/2, y=0 about z- axis. So surface area is:…

Q: For the conical surface 0 = 30°,0 <0< 21,0 <r< 2, the lateral surface area is what?

A: Sol

Q: Find the volume of the solid that lies within the sphere x2 + y² + z² = 64, above the xy-plane, and…

A: To find the volume if the solid within the given sphere above xy-plane and below the cone:…

Q: Evaluate T// y dV, where E is the portion of the sphere x² + y? + z² = 9 in the first octant (where…

A: Let, x=rsinθcosϕy=rsinθsinϕz=rcosθ

Q: Find the surface area of the portion of the sphere x² + y? + z² = 8 that is cut out by the cone z =…

A: The objective is to find the surface area of the portion of the sphere x2+y2+z2=8 that is cut out by…

Q: Determine the sections of the following surface on planes parallel to the xz plane. -y+ = 1 %3D O…

A: here first we solve for the surface and then check it .

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 the portion of the semi cone z = x2 + y? that lies between the planes z = 6…

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Q: Find the volume of the solid that is enclosed by the cone z = and the sphere x² + y2 + z2 = 72.

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Q: Find the area of the part of Sphere x? + y? + z? = 16 that is outside the paraboloid z=16 – x² – y?.…

A: The part of the object outside another object can be obtained by first calculating the intersection…