Exam 12: Extension G: Multiple Integrals

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Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius Use spherical coordinates to find the moment of inertia of the solid homogeneous hemisphere of radius   and density 1 about a diameter of its base. and density 1 about a diameter of its base.

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B

Find the mass of a solid hemisphere of radius 5 if the mass density at any point on the solid is directly proportional to its distance from the base of the solid.

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B

Use spherical coordinates. Evaluate Use spherical coordinates. Evaluate   ,where   is the ball with center the origin and radius  ,where Use spherical coordinates. Evaluate   ,where   is the ball with center the origin and radius  is the ball with center the origin and radius Use spherical coordinates. Evaluate   ,where   is the ball with center the origin and radius

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A

Identify the surface with equation Identify the surface with equation

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Use spherical coordinates to find the volume of the solid that lies within the sphere Use spherical coordinates to find the volume of the solid that lies within the sphere   above the xy-plane and below the cone   Round the answer to two decimal places. above the xy-plane and below the cone Use spherical coordinates to find the volume of the solid that lies within the sphere   above the xy-plane and below the cone   Round the answer to two decimal places. Round the answer to two decimal places.

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Identify the surface with equation Identify the surface with equation

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