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**jjoy****Guest**

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.

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

hi jjoy

Welcome to the forum.

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

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.

Bob

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

Thanks Stefy.

Bob

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

No problem.

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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