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

Answer 1

The Correct Option is D

The area of a circle is given by:
\[ A = \pi r^2 \] If \( A_1 : A_2 = x^2 : y^2 \), then:
\[ \frac{\pi r_1^2}{\pi r_2^2} = \frac{x^2}{y^2} \] Taking the square root:
\[ \frac{r_1}{r_2} = \frac{x}{y} \]