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The ratio of the radii of two circles is 4: 5. Find the ratio of their areas.

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Let the radii of the given circles be 4x and 5x respectively and let their areas be A1 and A2 respectively.

Then, A= πr2

= A1 = π × (4x)2

= A= 16πx2

And A= πr2

= A= π × (5x)2

= A2 = 25πx2

∴ (A1/A2) = (16πx2)/ (25πx2)

(A1/A2) = (16/25)

A1: A2 = 16: 25

Hence, the ratio of the areas of two circles is 16: 25

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