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If circumferences of two circles are equal, then what is the ratio between their areas?

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1 : 1

2 : 1

None of these

1 : 2

answer is A.

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Detailed Solution

Given that, circumference of two circles is equal.
We know that, circumference of a circle of radius r is equal to

2 π r

and area of a circle of radius r is equal to

π r 2

.
Let

r_{1}

be the radius of one circle and

r_{2}

be the radius of another circle.
Write the equation which display the relationship between the circles that their circumference are equal.

2 π r 1 = 2 π r 2

\Rightarrow

r 1 = r 2 = r s a y

Write the area of the circle with radius

r_{1}

A 1 = π r 12

Write the area of the circle with radius

r_{2}

A 2 = π r 22

Divide

A 1

A 2

and simplify.

A 1 A 2 = π r 22 π r 22

⇒ π r 2 π r 2

⇒ 11

If two circles has same circumference, then their areas are in the ratio

1 : 1

.
Hence the correct option is 1.

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