ratio

Here are two ways to think about it:

1. Let circle 1 have a radius of a, let circle 2 have a radius of b. if ratio of the areas is 4:1, then Pi*a^2/Pi*b^2=4/1 or a^2/b^2=4 or, taking the square root of both sides, a/b=2. But this turns out to be exactly what we're looking for. The ratio of the circumferences is (2*pi*a)/(2*pi*b)=a/b after cancellations. But we already know a/b=2, so the ratio of the circumferences must be 2:1

2. When two figures are similar (and all circles are similar to each other), the ratio of their areas is always the square of the ratio of their perimeters. And the circumference of a circle is essentially its perimeter. So if the ratio of the areas is 4:1 , the ratio of the circumferences must be the square root of that, or 2:1. I can elaborate more on why this is true if you're interested.

Ratio of area of 2 circles => (r1^2):(r2^2) ==> 4:1

Ratio of circumference of the 2 circles => r1:r2 => which is square root of (r1^2):(r2^2) => 2:1

Option D is the correct answer

Area1/Area2 = (pi*r1*r1)/(pi*r2*r2) = 4:1 => r1/r2 = square root(4/1) = 2

Circumference1/Circumference2 = (2*pi*r1)/(2*pi*r2) = r1/r2 =[spoiler] 2/1 - from above ! Hence Option D[/spoiler]

R - radius of one circle
r- radius of the other one
take the first statement n cross multiply.. u get pi*R^2 = 4*pi*r^2
take out pi & move the sq... R = 2r

since in the circumference (2*pi*r) .. 2 & pi dont matter (it comes down to only the radius)...
so the ratio is 2:1

D

apshara5 wrote:If the ratio of the area of two circles 4:1 what is the ratio of the circumference?
A. 16:1
B. 8:1
C. 4:1
D. 2:1
E. Can’t be determine

ans :d

When a problem asks for a ratio and has no fixed values, we can plug in our own numbers.

Let the area of the bigger circle = 4π.
r = 2.
C = 4π.

The area of the smaller circle = π.
r = 1.
C = 2π.

Bigger C : Smaller C = 4π:2π = 2:1.

The correct answer is D.

apshara5 wrote:If the ratio of the area of two circles 4:1 what is the ratio of the circumference?
A. 16:1
B. 8:1
C. 4:1
D. 2:1
E. Can’t be determine

ans :d

Let the radius of the 2 circles be a and b

So , ratio of the area of the 2 circles is -

pi*a^2 : pi*b^2 = 4:1

Hence a^2 : b^2 = 4:1

Or, a:b = 4 : 1


So we are now required to find the circumference of the 2 cicrles -

ie, 2*pi*a / 2*pi*b => a/b = 2:1


Now we find out from here and deduce that if -

The ratio of the area of two circles a^2:b^2 then the ratio of the circumference will be -

a : b


So we can make this a thumb rule as well , so that we can solve problems at a glance...

Hope this helps !!