If the Diameter of Circle C Is 3 Times the Diameter of Circle D


Question: If the diameter of circle c is 3 times the diameter of circle d, then what is the ratio of their areas?

The area of a circle is given by the formula: π/4 × (diameter)2

Answer: The ratio of the area of circle 'c' to the area of circle 'd' is 9:1

We will use the formula of the area of a circle to find the required ratio.

Explanation:

Let's assume the diameter of circle 'd' is 'x' units. Then the diameter of the circle 'c' is '3x'.

Area of circle 'c' = π/4 × (3x)2

Area of circle 'd' = π/4 × (x)2

(Area of circle 'c') / (Area of circle 'd') = (π/4 × (3x)2) / (π/4 × (x)2)

= 9 (π/4 × (x)2) / (π/4 × (x)2)

= 9 / 1

Therefore, the ratio of the area of circle 'c' to the area of circle 'd' is 9:1