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The ratio of the radii of two circles is 2:3. Find the ratio of their areas. If the area of the bigger circle is 3123 cm². Find the area of the smaller circle.

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1440 cm²

1388 cm²

1500 cm²

1240 cm²

answer is B.

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Detailed Solution

Let the radius of smaller circle ‘r’ and the bigger circle is ‘R’.
Ratio –
⇒r : R = 2 : 3
⇒A₁ = πr²
⇒A₂ = πR²
According to question – ⇒

\frac{A^{1}}{A^{2}} = π \frac{{(2)}^{2}}{(3) ²}

⇒

\frac{A^{1}}{3123} = \frac{4}{9}

⇒A₁ = 1388cm²
The area of smaller circle A₁ = 1388cm².

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