If the ratio of the areas of two circles is 4:1, what is the ratio of

Question

If the ratio of the areas of two circles is 4:1, what is the ratio of their circumferences?

A. 2:1
B. 3:1
C.  \pi:1 
D. 4:1
E. 8:1

Paras96 · Answer

Let the radius of circles be R and r respectively

According to the given, question

πR^2 : πr^2 = 4:1
=> R : r=2:1

we need to find the ratio of circumference which can be given as 
=> 2πR:2πr = R:r=2:1

Hence A

Kinshook · Answer

Asked: If the ratio of the areas of two circles is 4:1, what is the ratio of their circumferences?

Area A  = \pi rˆ2

A1/A2 = r1ˆ2/r2ˆ2 = 4/1

r1ˆ2/r2ˆ2 = 4/1

r1/r2 = 2/1

r1:r2 = 2:1

IMO A

walterwhite756 · Answer

Ratio of Area = 4:1
Ratio of Radius = 2:1
Ratio of Circumference = 2:1

IMO A.

CrackverbalGMAT · Answer

Hi pgocegon Great to e-connect !

On a GMAT question, analysis is your key tool! Think about it this way- This practice question assesses your ability to apply fundamental GMAT Geometry concepts and understand the relationship between areas and circumferences of circles. It aligns with the GMAT's emphasis on logical reasoning and efficient problem-solving skills using just basic/core concepts.

So, what are the GMAT conceptual insights here ? Recall that the area of a circle is directly proportional to the square of its radius, while the circumference is directly proportional to the radius.

So, what strategies can you quickly think of to apply here? Since the ratio of areas is 4:1, the ratio of their radii is the square root of 4:1, which simplifies to 2:1. Then what do you do with this information? Can you use it somewhere with a smart value? GMAT is about thinking fast and smart!!

Take a plugin value of the radius of the first circle as 2 units, and the second circle's radius as 1 unit based on the 2:1 ratio. Once you come up to this, how do you close with the solution?

Operate with the data! Apply the formula for circumference: C = 2πr. For the first circle (radius = 2 units): C₁ = 2π*(2) = 4π units For the second circle (radius = 1 unit): C₂ = 2π*(1) = 2π units

Close the problem The ratio of their circumferences is C₁ : C₂ = 4π : 2π = 2:1.

Did you Analyze the traps? You can fall for the trap of B or D if you attempt to use a direct relationship between the area and circumference ratios, without fully understanding the concept that the ratio of areas is related to the square of the ratio of radii. Critical thinking and a clear understanding of the connections between areas, radii, and circumferences will lead you to the correct answer of 2:1 (Choice A). Don't just focus onpractice but practice with analysis for every question. Even the simplest of the GMAT questions have a lot to teach us

Keep the learning up

Let me know if you face any concerns while going through my post. Devmitra Sen Head of Academics,Crackverbal Connect with me on LinkedIn here

If the ratio of the areas of two circles is 4:1, what is the ratio of

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If the ratio of the areas of two circles is 4:1, what is the ratio of

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