Question

The ratio of radius of two circles is 1 ∶ 4, what will be the ratio of the areas of the circle?

1. 1 ∶ 4
2. 1 ∶ 16
3. 16 ∶ 1
4. 4 ∶ 1

Answer 1

Correct Answer - Option 2 : 1 ∶ 16

Given:

Ratio of the radius of the circles = 1 ∶ 4

Formula used:

Area of the circle = πr² 

Calculation:

Let the radius of the circles be x and 4x units

Area of circle₁ = πx² 

Area of circle₂ = π(4x)² 

Ratio of areas = πx2 ∶ π(4x)2 

⇒ Ratio of area = x² ∶ 16x² 

∴ Ratio of the area of the two circles is 1 ∶ 16