Question

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

Answer 1

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

Then, A₁ = πr²

= A₁ = π × (4x)²

= A₁ = 16πx²

And A₂ = πr²

= A₂ = 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