Find d, the outer diameter

[god_is_atheist]

Here is the answer I got.
t, thickness
d, diameter
A=pi/4*[d^2-(d-2t)^2]
d=2A/(sqrt pi)d-2t

When I entered the values I suspected that I derived the outer diameter incorrectly.

 

[lev888]

Please post the entire problem.

 

[topsquark]

Please post any problem. You seem to think we are psychic!

-Dan

 

[HallsofIvy]

You are given A=pi/4*[d^2-(d-2t)^2] which is ambiguous. It could be \(\displaystyle A= \frac{\pi}{4[d^2- (d- 2t)^2]}\) or
\(\displaystyle A= \frac{\pi}{4}[d^2- (d- 2t)^2]\)

I suspect it is the latter. If so then \(\displaystyle \frac{4A}{\pi}= d^2- (d^2- 4td+ 4t^2)\)
The "\(\displaystyle d^2\)" terms cancel.

\(\displaystyle \frac{4A}{\pi}= 4td+ 4t^2\)
\(\displaystyle \frac{4A}{\pi}+ 4t^2= 4td\)

\(\displaystyle d= \frac{\frac{4A}{\pi}+ 4t^2}{4t}= \frac{A}{t\pi}+ t\).

 

[god_is_atheist]

I see my mistake.

 

[HallsofIvy]

That God is not an atheist?