Question

the ratio of the radii of two circles is 5:2. what is the ratio of their areas? 5:2 25:4 25:2 5:4 3:1

Explanation:

Step1: Define radii using ratio

Let the radii be $r_1 = 5k$ and $r_2 = 2k$ where $k>0$.

Step2: Calculate area of each circle

Area of circle 1: $A_1 = \pi r_1^2 = \pi (5k)^2 = 25\pi k^2$
Area of circle 2: $A_2 = \pi r_2^2 = \pi (2k)^2 = 4\pi k^2$

Step3: Find ratio of areas

$\frac{A_1}{A_2} = \frac{25\pi k^2}{4\pi k^2} = \frac{25}{4}$

Answer:

25:4