Given that the circumference of a circle is 99 and taking ''PIE;; as 22/7 ? How to calculate the diameter of the circle

Question

Want to calculate the diameter of a circle if the circumference is 99 cm. [Taking 'PIE' as 22/7]

Answer 1

This question uses what I call "magic numbers."  They make the calculations easy so you can concentrate on solving the problem.  This is important for (1) estimating/checking answers, (2) understanding the process and not simply "following the steps", (3) providing alternative methods when continuous improvement processes are used.
 
So, first, I must comment on Kenneth S.'s answer.  Think: if π=C/d, what is the circumference a circle with diameter 7?  Using π=22/7=C/7, then C=22 [done!]  To be somewhat more accurate (if that is even necessary),
     C = πd = (3.1415926)(7) ≅ 21.99
If I'm working on most home materials, 0.01 inch is hardly noticeable.
Did anyone realize that the definition of π is C/d ??
Now, a wild example that uses "a little more than 3" (which is even further from the real π.)  I was sewing the hem in an 8-ft banner and wanted to know how much of a fold I should make for it to fit rather snugly around a 5/8" pipe.  Well. I reasoned (with no calculator), the circumference is (5/8)π which is a little more than 15/8", so 2" will fit snuggly.  I'll make a 1" fold and sew there.
Then, using computers to solve problems, we often want a "first/rough guess" or "an order of magnitude" to plan.  After doing a feasibility study, we would like more precise estimates and we might make a rough prototype [you realize that absolutely nobody flies an airplane that has not already had each part broken by testing (or simulation)].  For example, "Estimate the cost of a house plan based solely on the number of square feet; refine the cost estimate as decisions are made about schedule, materials, modifications, etc.; further refine the costs based on the market, competition, etc.; bid on the project (with allowable cost adjustments, of course)...   Nobody spends all this time planning if they don't expect to actually do the work.
Estimating/checking is also limited by time when taking standardized tests !!
 
So, I recommend that you not mention any complaints about this problem ... it is quite valuable in its current form.
 
O.K. the problem:
     π = C/d           [definition]
    22/7 = (99)/d     [givens in problem]
     (22/7)d = 99      [multiply both sides by d;  or else you could cross-multiply]
        d = (99)(7/22)   [multiply both sides by π;   or we could start with d=C/π;
                                      remember: to divide by fraction, invert and multiply]
       d = (9)(7/2)   [cancel an 11]
       d = 31 1/2    [special note:  using π=3.14159, d=31.51271
                PLZ judge -- is that close enough?]

Answer 2

For the life of me, I cannot see why anyone still uses the crude 22/7 as "PI".  We live in an era of calculators which know pi to many decimal places, and ignoring calculators and the possibility of getting answers very close to 'exact' seems to be within everyone's reach.  And you can tell your teacher what I'm saying in this paragraph, too.*

 

Anyway, C = 2(pi)(radius) OR C = (pi)(diameter).  From the latter, it follows that diameter = C ÷ pi.

 

So just divide circumference by pi, THEN round answer to any desired accuracy.

 

*  Note 22/7 is RATIONAL but pi is definitely NOT RATIONAL, i.e. it CANNOT be represented as any ratio of two integers.

    To 4 decimal places, pi is about 3.1416