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.
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