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#1 2014-07-26 06:02:59

jjoy
Guest

3d geometry?

A sphere with radius 3 is inscribed in a conical frustum of slant height 10. (The sphere is tangent to both bases and the side of the frustum.) Find the volume of the frustum.

#2 2014-07-26 11:50:56

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: 3d geometry?

hi jjoy

Welcome to the forum.

The algebra is messy but it should work.  Sorry, I cannot find a simpler method.

agDmZc1.gif

Two tangents to a circle from a point will be equal.

Then the small (removed) cone will be in the same proportion as the large cone.  Hence:

I don't have a simple solution to these, but someone else on the forum will probably put the equations through a computer for us and come up with values for x and y.

Then it should be easy (?) to compute the volume.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2014-07-27 01:16:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,387

Re: 3d geometry?

Hi jjoy and Bob


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#4 2014-07-27 05:37:38

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: 3d geometry?

Thanks Stefy.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2014-07-27 07:53:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,387

Re: 3d geometry?

No problem. smile

The volume is now easy to compute.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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