(c) Consider a finite cone with its tip at the origin facing towards the decreasing z direction and its base at z=h where it has a radius of a. If a sphere of radius 2a is dropped into the cone from above (resembling a scoop of ice cream in a cone) setup a triple integral in cylindrical coordinates for the volume of the sphere inside the cone. You are not required to solve this integral.

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Chapter2: Second-order Linear Odes
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C)
surface of the paraboloid z = 2² + y² using cylindrical coordinates.
(c) Consider a finite cone with its tip at the origin facing towards the decreasing z direction
and its base at z = h where it has a radius of a. If a sphere of radius 2a is dropped
into the cone from above (resembling a scoop of ice cream in a cone) setup a triple
integral in cylindrical coordinates for the volume of the sphere inside the cone. You
are not required to solve this integral.
Transcribed Image Text:surface of the paraboloid z = 2² + y² using cylindrical coordinates. (c) Consider a finite cone with its tip at the origin facing towards the decreasing z direction and its base at z = h where it has a radius of a. If a sphere of radius 2a is dropped into the cone from above (resembling a scoop of ice cream in a cone) setup a triple integral in cylindrical coordinates for the volume of the sphere inside the cone. You are not required to solve this integral.
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