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**johny****Member**- Registered: 2005-11-19
- Posts: 34

Well i have got this problem about re-arranging the following formula:

V=1/3*Pi*r2*h - 1/3*Pi*r2/3*h/3

Can anyone re-arrange to get r or r square please???

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

All of the /3's in the second term can be combined into a /27.

V = 1/3πr²h - 1/27πr²h

These two terms are now identical apart from the constant at the front, so they can be combined:

V = 8/27πr²h

To get r² on its own, divide the right-hand side by everything except it:

27V/(8πh) = r²

To get r, just square root both sides:

√[27V/(8πh)] = r

Why did the vector cross the road?

It wanted to be normal.

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**johny****Member**- Registered: 2005-11-19
- Posts: 34

Thanks alot mathyperson.

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**johny****Member**- Registered: 2005-11-19
- Posts: 34

HERES A SIMPLIFICATION I AM UNABLE TO DO, ITS OF THE SAME QUESTION:

S.A.= Pi*R* Square of [R2 + 2025/Pi*R2]

---The term in bracket is Square-----

So is there anyway to simplify this more??? Please i really need quick help.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,664

Surface Area?

Does this relate to your question I got part way through here: http://www.mathsisfun.com/forum/viewtopic.php?id=2002 ?

I am sorry, I just haven't had time to finish it.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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

That can't be a measure of surface area.

Every term in a surface area formula has to include exactly 2 lengths.

πr only has 1 length and (r² + 2025/πr²)² is either a contradiction in itself, or it contains 4 lengths, which would be impossible anyway. Are you sure the formula is right?

Why did the vector cross the road?

It wanted to be normal.

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**johny****Member**- Registered: 2005-11-19
- Posts: 34

Mathsyperson: Your right this isnt the formula for the Surface area.........but according to my question i had to substitute the height H of Volume to the surface area.

as the formula is S.A= Pi*R*S ...........and s= square of [R2+H2]......so i substituted the height in this formula. Which came to the above term. can it be simplified more???

*Last edited by johny (2005-11-27 21:02:57)*

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

In my previous post, I must have imagined that you had a plus sign in there, which you didn't. There's actually only one term, but it has 5 lengths, which is still wrong.

If you square rooted the bit inside the square brackets then you would get 2 lengths, which is perfect.

S.A. = π*r*√[r² + (2025/π)r²]

That can be simplified more by combining the two terms inside the bracket to give [(2025/π+1)r²]

The r² can then be taken out of the square root:

S.A. = π*r²√(2025/π+1)

Why did the vector cross the road?

It wanted to be normal.

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