The areas of two circles are in the ratio 16 : 36. What is the ratio of their radii?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2 : 3
The area of a circle is \(\pi r^2\), so the ratio of areas is the square of the ratio of radii. The ratio of radii is therefore the square root of the ratio of areas.
\(\pi r_1^2:\pi r_2^2=16:36\), so \(r_1^2:r_2^2=16:36\)
\(r_1:r_2=\sqrt{16}:\sqrt{36}=4:6\)
\(4:6=2:3\)