Let A denote the area of a circular region. Which of the following

Question

Let A denote the area of a circular region. Which of the following denotes the circumference of that circular region?

(A)  \sqrt{\frac{A}{\pi}}

(B)  2\frac{A}{\sqrt{\pi}}

(C)  2\pi \sqrt{A}

(D)  2\sqrt{\frac{A}{\pi}}

(E)  2\pi \sqrt{\frac{A}{\pi}}

Source:   Nova GMAT  
Difficulty Level:   550

quantumliner · Answer

Let radius of the circle = r

Area of circle =  \pi  r^2 
Circumference of circle = 2 \pi r

Now given

Area of circle = A

A =  \pi  r^2

r = \sqrt{A/\pi}

Circumference = 2 \pi  \sqrt{A/\pi}

Answer is E

sashiim20 · Answer

Let the radius of circular region be  = r

Area of circular region,  A =   \pi  r^2

r^2   = \frac{A}{\pi}

r =\sqrt{\frac{A}{\pi}}  ------------- (i)

Circumference of circular region,  C = 2  \pi  r  ------------ (ii)

Substituting value of  r  from (i) in (ii), we get;

C = 2\pi\sqrt{\frac{A}{\pi}}  . Answer (E)...

pushpitkc · Answer

Assume radius(R) of the circle to be 7.
It is known that Pi = 22/7

Area of the circle is 154, as area is Pi*R^2, 
the circumference will be 2*Pi*R or 44.

Only Option E, 2*Pi*sqrt(A/Pi) = 2*Pi*sqrt(49) = 2*22/7*7 = 44.
Hence, Option E is our answer.

singhabhijeet · Answer

option E.

Area of circle =  \pi  * r^2

Circumference of Circle = 2 \pi r

As per the condition provided in question:

\pi  * r^2  = A

r =  \sqrt{{\frac{A}{\pi}}}  ----- eq 1

Using eg 1 and circumference formula

2 \pi r = 2  \pi   \sqrt{{\frac{A}{\pi}}}

JeffTargetTestPrep · Answer

We can let r = the radius of the region and we have:

A = (r^2)π

A/π = (r^2)

√(A/π) = √r^2

√(A/π) = r

Thus, the circumference is 2π√(A/π).

Answer: E

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Let A denote the area of a circular region. Which of the following

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Let A denote the area of a circular region. Which of the following

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