Question

The ratio between the areas of two circles is 16 : 9. Find the ratio between their :
(i) radius
(ii) diameters
(iii) circumference

Answer 1

(i) Let radius of first circle = r₁

and radius of second circle = r₂

Given that ratio of the areas of circles = 16 : 9

⇒ `(π"r"_1^2)/(π"r"_2^2)=16/9`

⇒ `(π"r"_1^2)/(π"r"_2^2)=4^2/3^2`

⇒ `("r"_1)/("r"_2)=4/3`

(ii) Let the diameter of first circle = d₁

and diameter of second circle = d₂

Since, we know that diameter = 2 × radius

∴ d₁ = 2 × r₁ = 2 × 4x = 8x

and d₂ = 2 × r₂ = 2 × 3x = 6x

Now, the ratio between the diameter of two circles = d₁ : d₂

= 8x : 6x = 4 : 3

(iii) Now, consider the ratio of circumference of the circles

= `(2π"r"_1)/(2π"r"_2)="r"_1/"r"_2=4/3`

∴ The ratio between the circumference of two circles = 4 : 3