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Answer to each blank to correctly complete the explanation for deriving the formula for the volume of a sphere.

 

 

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius r and height ________ minus the volume of two cones, each with a radius and height of r. A cross section of the sphere is __________, and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is __________.

The volume of the cylinder with radius r and height 2r is  2πr3

, and the volume of each cone with radius r and height r is _________ . So the volume of the cylinder minus the two cones is  43πr3 . Therefore, the volume of the cylinder is ___________ by Cavalieri's principle.

wertyusop  Jan 19, 2018
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Go online to this page, which explains the derivation of the volume of the sphere very well:

http://mathcentral.uregina.ca/qq/database/qq.09.01/rahul1.html

Guest Jan 19, 2018
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What is your problem wertyusop?

 

Someone is kind enough to give you an answer, you give no written response but give them a thumbs down. That is plain rude!

 

If you do not like an answer then you politely state why.  Then maybe you will get more help in a form that is useful to you. 

 

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Thanks you for you answer guest, it looked good to me. 

 I was wondering whether wertyusop wanted a calculus answer or some other answer... He/she did not specify. 

Melody  Jan 20, 2018
edited by Melody  Jan 20, 2018
edited by Melody  Jan 20, 2018
edited by Melody  Jan 20, 2018

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