The circumferences of two circles are in the ratio 2:3. What is the ra

1.	The circumferences of two circles are in the ratio 2:3. What is the ratio between their areas?
Answer» Ratio of circumferences of two circles = 2:3 (given) Let the two circles be C₁ and C₂with radii r₁ and r₂. Circumference of circle = 2πr Circumference of C₁ = 2πr₁ and Circumference of C₂ = 2πr₂ (Circumference of C₁) / (Circumference of C₂) = (2πr₁)/(2πr₂) 2/3 = r₁/r₂ Now, (area of C₁) / (area of C₂) = (πr₁²)/(πr₂²) = {(r₁)/(r₂)}² = (2/3)² =4/9 Therefore, the required ratio is 4:9.

The circumferences of two circles are in the ratio 2:3. What is the ratio between their areas?

Answer»

Ratio of circumferences of two circles = 2:3 (given)

Let the two circles be C₁ and C₂with radii r₁ and r₂.

Circumference of circle = 2πr

Circumference of C₁ = 2πr₁ and

Circumference of C₂ = 2πr₂

(Circumference of C₁) / (Circumference of C₂) = (2πr₁)/(2πr₂)

2/3 = r₁/r₂

Now,

(area of C₁) / (area of C₂) = (πr₁²)/(πr₂²)

= {(r₁)/(r₂)}²

= (2/3)²

=4/9

Therefore, the required ratio is 4:9.