8. Find the volume bounded between a sphere of radius 2, a cylinder of radius 2, the x-y plane, and the plane z =2 using a triple integral. You may use either rectangular, spherical, or cylindrical coordinates for your integral, and you may use technology to evaluate your integral.

Q: Find the surface area of the part of the sphere x² + y² + z² = 81 that lies above the cone z =…

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

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Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

Q: Find the volume of the wedge cut from the first octant by the cylinder z = 45-5y² and the plane x +y…

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Q: A pipe was cut into two and looks like this as attached in the picture.  Imagine both circle have a…

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Q: Use a triple integral in spherical coordinates to derive the volume of a sphere with radius a.

A: To find - Use a triple integral in spherical coordinates to derive the volume of a sphere with…

Q: The geometry is defined by the blue surface. x₁-2 cm, x2=6 cm, x3 10cm and y₁=6 cm. y₁ ус с x 202 1)…

A: As per the Bartleby Policy, we can answer for only the first question. Please repost the whole…

Q: In cylindrical coordinates, find the volume of the solid S enclosed by the cone and the sphere as…

A: Given : the cone z=r and the upper hemisphere z=2-r2.

Q: Find the surface area of the part of the sphere x² + y² + z² = 16 that lies above the cone z = √√x²…

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Q: Explain why the explicit description for a cylinder x2 + y2 = a2 cannot be used for a surface…

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Q: .10π Sr Sa 0 0 (1 - sin o)/2 -л(157-16) A) (1 - cos p)/2 48 5 C) 7(157 - 16) 96 o² sin o do do de 5…

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Q: Use explicit description of the surface to evalue the integral.

A: Step 1: it is provided that, there is a surface integral∫∫(x+yz)dSwhere S:z=−x−2y+4 on…

Q: Use cylindrical coordinates to find the volume of a sphere of radius a from which a central cylinder…

A: The equation for the sphere in cylindrical coordinate system is r2+z2=a2. where, b ≤ r ≤ a and…

Q: Evaluate the cylindrical coordinate integral. 10 20 r 8 dz r dr d0 2 8 0 0 O A. 144 О в. 48 Ос. 96…

A: Solution

Q: The semicircle above the x-axis centered at origin with a radius=1 is rotated about x-axis to create…

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Q: Use either a computer algebra system or a table of integrals to find the exact area of the surface…

A: Solution

Q: Find the surface area of the part of the sphere x? + y² + z? = 4 that lies above the cone z = I² +…

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Q: 1 27 1+sin(0) 2r dr d0 dz -1 0

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Q: Find the surface area of a sphere of radius 4 using integral.

A: this is the question of area is given we have to find the area of sphere whose radius = 4 given and…

Q: 5. Z = -y A r = 3 cos 0 %3D

A: In general, volume integrals are triple integrals, which involve the integral with respect to x,y,…

Q: volume of the ellipsoid

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Q: Explain why triple integrals that represent the volumes of solids are sometimes easier to evaluate…

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Q: The base of a sand pile covers the region in the xy-plane that is bounded by the parabola x2 + y = 6…

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