i was looking for this problem

http://www.majortests.com/gre/problem_solving_expl.php?exp=50313039243130243330 and was surprised if it is correct,we know that circumference or perimeter of circle is equal to $C=\pi*D=2*\pi*R$ but what about perimeter of half circle?i found following link http://www.mathvillage.info/node/159

which says that perimeter of half circle is $c=\pi*D/2+D$

where $D$ is diameter of course,but in problem,link of which i have posted,it is not considered and it said that perimeter of half circle is just $\pi*D/2$,in case of this test come on GRE exam,i should now of course which formula is correct,so please help me to determine there is error made in formula $\pi*D/2+D$ or what? thanks in advance


In the linked question, we are just interested in the upper half of the circle and not at all the base (diameter). So, that is why we are just using the perimeter as $\pi*r$.

Every formula is used in certain context. And understanding context is more important than the formula.

ADDED- Perimeter can be considered as the length of a tape required to cover the given figure. So, now i guess you can see which formula is to be used.

  • $\begingroup$ so could you explain it more detailed? $\endgroup$ – dato datuashvili Jul 30 '13 at 10:20
  • $\begingroup$ i could not understand one thing,perimeter of white region is equal to perimeter of rectangle minus perimeter of half circle right? $\endgroup$ – dato datuashvili Jul 30 '13 at 10:22
  • $\begingroup$ In the question, had they asked to find out the perimeter of the half circle/ perimeter of the shaded region, that sure would have been &\pi*r+2r& $\endgroup$ – Ramit Jul 30 '13 at 10:24
  • $\begingroup$ But we are asked to find the perimeter of the part which is not shaded. which is equal to 3 sides of the rectangle + arc of the half cicle $\endgroup$ – Ramit Jul 30 '13 at 10:27
  • $\begingroup$ note that full perimeter of the half circle is not equal to the perimeter of the arc. or for that matter, full perimeter of the half circle is not equal to the perimeter of the base. I hope i am clear. $\endgroup$ – Ramit Jul 30 '13 at 10:28

The perimeter of a semicircle is, in fact, $\pi * \frac{D}{2} + D$. There is the $\pi * \frac{D}{2}$ portion coming from the curved part, which is half of the total perimeter of a circle, as would be expected, and there is the $D$, which comes from the flat side of the semicircle, which, as it is a diameter of the circle, clearly has length $D$.

  • $\begingroup$ so it means that,solution is wrong right? $\endgroup$ – dato datuashvili Jul 30 '13 at 10:16
  • $\begingroup$ It means that which solution is wrong? $\endgroup$ – qaphla Jul 31 '13 at 5:39

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