What is the circumference of circular region R? (1) The area of R is

Question

What is the circumference of circular region R?

(1) The area of R is 36  \pi

(2) The area of a square region inscribed in R is 72.

chetan2u · Answer

We are looking for circumference. 
what do we require - RADIUS

(1) The area of R is 36  \pi 
we can get the RADIUS. 
A= \pi*r^2=36*\pi ..
so r=6.
sufficient

(2) The area of a square region inscribed in R is 72.
so the diagonal of square will be the DIA of circle..
so  x^2=72......x=6\sqrt{2} 
diagonal of square =  6\sqrt{2}*\sqrt{2}=12 
so DIA = 12 and so R = 12/2=6
suff

D

anuj04 · Answer

1. Area is 36π = π r^2. Therefore r=6 . We can now calculate 2 πr –  Sufficient 
 2. The area of a square region inscribed in R is 72. i.e. side of square is √72 = 6√2. Therefore, its diagonal is 6√2*√2=12. Therfore, r=6. We can now calculate 2 πr –  Sufficient 
Both statement is sufficient alone. Answer is D

anupam87 · Answer

Hi  Bunuel ,

When we say that a square is inscribed in a circle, is it true in all cases that the 4 vertices of the square will always be on the circle? Can we have a square in which may be 3 vertices of the square are on the circle?

I know this is a very basic question, but I had made a similar mistake earlier in one of a data sufficiency question.

Thanks!!

Bunuel · Answer

A polygon is inscribed in a circle means that all of its vertices are on the circumference.

Shorub · Answer

To find the circumference of the circular area, we need the radius

Statement 1 - Radius can be arrived from the given value for area

36π=πr^2

Statement 2 - since the square is inscribed, 
the diagnols of the square = diameter of the circular area

Using area of square, side of square can be determined.

Using side of the square, diagonal can be determined.

Using diagonal, diameter / radius of the circular area can be determined.

Hence, both statements are sufficient. IMO option D

Posted from my mobile device

Archit3110 · Answer

#1
r=6
suffiecient
#2
s=6√2
diagonal = diameter= 12; radius = 6
sufficeint
IMO D

bumpbot · Answer

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What is the circumference of circular region R? (1) The area of R is

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