In cylindrical coordinates, find the volume of the solid S enclosed by the cone and the sphere as shown, where z = r, and the upper hemisphere is the sqrt(2-r²): (0,0,√2) X x² + +y²+z² = 2 2 Z=√x + y

Q: given ∫∫s (x2z) dS and S is the part in z = sqrt(x2+y2), which lies in x2+y2 = 1 calculate the…

A: we have to evaluate ∬Sx2zdS Now, we have z=x2+y2 ⇒z2=x2+y2∂z∂x=xz and…

Q: Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone z = x² + y2…

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Q: Use cylindrical coordinates. Find the volume of the solid that lies between the paraboloid z = x2 +…

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Q: Use spherical coordinates to find the volumes of the two solids obtained when the hemisphere z =…

A: Let  x=rsinθcosφy=rsinθsinφz=rcosθJ=∂x,y,z∂r,θ,ϕ=r2sinθdrdθdϕ The plane x=3 divide the hemisphere…

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: A wedge is cut out of a circular cylinder of radius 14 by two planes. One plane is perpendicular to…

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Q: Find the volume of the solid enclosed by the parabolics Z= 4CX²+y²² Jand 2 = 32- 4(x² + y²)

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Q: Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder  x2 +…

A: To find the volume of the solid that lies within both the cylinder and the sphere.…

Q: Find the volume of the solid that lies within both the cylinder x² + y² = 4 and the sphere x² + y² +…

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Q: Use cylindrical coordinates to determine the volume of the solid that is enclosed by the cone z =…

A: Volume by cylindrical coordinates