12. Use cylindrical coordinates to find the volume of the solid inside the sphere x² + y² + z² = 16 and outside the cone z = x² + y².

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

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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: 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: 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: Find the volume V which lies inside the sphere x + y' +(z – 5)² = 25 and outside the sphere x? + y?…

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

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Q: Use spherical coordinates to find the volume of the top half of the sphere x? + y? + z? = 4 that…

A: Given that a sphere x2+y2+z2=4 and a cone is z2=x2+y2 We have to find the volume of the top of the…

Q: Find the volume of the solid region which lies inside the sphere x² + y? + z² = 4z and outside of…

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Q: Find, using Cylindrical Coordinates, the volume of the solid that is enclosed by the cone and the…

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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: Use polar coordinates to find the volume inside the cone z = 2 - x² + y² and above the xy-plane.

A: Obtain the volume inside the cone z=2-x2+y2 and above the xy-plane. Find the equation of the circle…

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 volume of the solid obtained by rotating the triangle (2,0)(2, 4)(1, 1) about the…

A: Solution :-

Q: Express the volume of the solid lying inside the sphere r2 + y? + 22 8 and outside the cylinder ? +…

A: Given:  Solid lying in a sphere x2+y2+z2=16 and outside the cylinder  x2+y2=2