Find the volume V of the solid E that lies above the cone z = x² + y² and below the sphere x2 + y2 + z² = 64.

Q: Find the surface area of the part of the plane z = 4 + 2x + 3y that lies inside the cylinder z² + y²…

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

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Q: Find the volume of the tetrahedron bounded by coordinate planes (x>=0, y>=0,z>=0) and the plane…

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Q: 6) Find the area of the part of the sphere X² + y² + Z² = 4 that lies within the cylinder X² + y² =…

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Q: Calculate the volume of the solid which lies above the cone 3z2 = x2 + y² and below the sphere (x –…

A: Given solid lies above the cone 3z2=x2+y2 and below the sphere x-22+y2+z2=4

Q: Find the surface area of the part of the plane z = 6 + 4x + 7y that lies inside the cylinder x² + y²…

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Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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Q: iv) The region bounded by the semi-circle x = centroid (x,y). a) Explain why y = 0. b) Find the…

A: The objective of this question is to find the centroid of the region bounded by the semi-circle x =…