Question

The ratio of the areas of two circles is \( x^2 : y^2 \). Then the ratio of their radii is

• A. \( x^2 : y^2 \)
• B. \( \sqrt{x} : \sqrt{y} \)
• C. \( y : x \)
• D. \( x : y \)

Hint:

The ratio of areas of two circles is the square of the ratio of their radii.

Answer 1

The Correct Option is D

Step 1: The area of a circle is proportional to the square of its radius, i.e., \( \text{Area} \propto r^2 \). Step 2: If the ratio of areas is \( x^2 : y^2 \), then the ratio of their radii is \( x : y \). Thus, the correct answer is \( \boxed{x : y} \).