Question

the circumference of two circles are in the ration 4:6 find the ratio of their areas

Answer 1

Answer :

The required ratio is 4 : 9

Step-by-step explanation :

Circumference of 1st circle / circumference of 2nd circle = 2 π r / 2 π r

⇒ 2 π R / 2 π r = 4 / 6

⇒ R / r = 4 / 6

⇒ R : r = 4 : 6

On squaring both sides,

⇒ R² : r² = 4² : 6²

⇒ R² : r² = 16 : 36

⇒ R² : r² = 4 : 9

Therefore, π R² : π r² = 4 : 9.

Answer 2

Let the radii of the two circles be r and R respectively.

Then their circumferences will be 2πr and 2πR

Hence 2πr : 2πR = 4:6 so that r:R = 4:6

Squaring r^2:R^2 = 16:36

Ratio of their areas πr^2:πR^2 = r^2:R^2 = 16:36 ➡4: 9

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