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#1 2006-10-24 09:17:25

Prakash Panneer
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Registered: 2006-06-01
Posts: 110

Volume

How will you prove the volume of the cone is one-third of the volume of the cylinder?

dunnoThanks in Advance up


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#2 2006-10-24 10:52:19

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Volume

you can think of it as solid of revolution.

for a cone of height h, and radius r.

you have


so the volume of the cone is

and ofcourse, volume of the cylinder is

by the rule of finding the volume of a prism, in this case the cross section is a circle, of whos area is

Last edited by luca-deltodesco (2006-10-24 10:53:27)


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#3 2006-10-24 11:59:20

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Volume

Are you looking for a geometric or calculus argument?


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#4 2006-10-24 12:09:59

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

Re: Volume

Geometric proof.up


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#5 2006-10-25 00:33:28

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Volume

Can you just say that the volume of a cone is known to be 1/3πr²h and the volume of a cylinder is known to be πr²h and just divide the two?

That's a bit trivial though, so you probably wanted to actually find the volumes of each solid.


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#6 2006-10-25 05:26:19

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

Re: Volume

I want the Geometric proof.

Can anyone help?

Please....


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#7 2006-10-27 06:14:13

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

Re: Volume

Is there any practical method?


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#8 2006-10-29 13:17:11

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: Volume

There is.
This follows immediately from the fact that the volume of a pyramid is exactly 1/3 of the volume of the prism, which can be proved by suitable disection of the prism into 3 pyramids, which must have equal volumes by the Cavalery (the name may be spelled incorrectly) principe.


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