Consider a sphere with radius r. Consider horizontal (or vertical) slices through the sphere such that...

 

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Consider a sphere with radius r. Consider horizontal (or vertical) slices through the sphere such that the slices are cylinders with very small height Ah. Compute the following: 1) What is the volume of each slice? 2) Write a Reimann sum that uses the volume of each slice to approximate the volume of the sphere. 3) Use the result from part (2) to write the definite integral representing the volume of the sphere of radius r. Then, compute the integral to derive the volumme of a sphere of radius r. Consider a sphere with radius r. Consider horizontal (or vertical) slices through the sphere such that the slices are cylinders with very small height Ah. Compute the following: 1) What is the volume of each slice? 2) Write a Reimann sum that uses the volume of each slice to approximate the volume of the sphere. 3) Use the result from part (2) to write the definite integral representing the volume of the sphere of radius r. Then, compute the integral to derive the volumme of a sphere of radius r.

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1 Volume of each slice since the slices are cylindilical ... View the full answer