What is the ratio of the radio of two circles?

Question

The ratio of the areas of two circles is 121/100. What is the ratio of the radio of the two circles?

Answer 1

Hi Dazzmine. You are given the ratio of the areas of two circles, and you are asked to find the ratio of the radii. To solve this problem, you need an expression that relates the area of a circle to its radius. The formula for the area of a circle is

A = π r²

when A is the circle's area and r is the radius.

Define one circle's area to be A₁, and the other circle's area to be A₂. You are told that A₁/A₂ = 121/100.

You can express the circle's area in terms of its radius.

A₁ = π r₁² and A₂ = π r₂²

Next, you can plug these expressions into A₁/A₂ = 121/100.

A₁ /A₂ = π r₁² / π r₂²

A₁ /A₂ = r₁² / r₂²

A₁ /A₂ = 121/100

You can take the square root of both sides of the equation r₁² / r₂² = 121/100 to find the ratio of the radii

√(r₁² / r₂²) = √(121/100)

r₁ / r₂ = 11/10

The ratio of the radii is 11/10.