Question

The circumferences of two circles are in the ratio 3:2, then the ratio of their areas will be:

• A. 7:9
• B. 4:9
• C. 2:3
• D. 9:4

Hint:

The ratio of the areas of two circles is the square of the ratio of their radii (or circumferences).

Answer 1

The Correct Option is B

We are given that the circumferences of two circles are in the ratio \( 3:2 \). The formula for the circumference of a circle is given by: \[ C = 2\pi r \] where \( r \) is the radius of the circle.
Step 1: Relating the circumferences to the radii.
The ratio of the circumferences is: \[ \frac{C_1}{C_2} = \frac{3}{2} \] Since the circumferences are proportional to the radii, we can write the ratio of the radii as: \[ \frac{r_1}{r_2} = \frac{3}{2} \]
Step 2: Ratio of the areas.
The area of a circle is given by the formula: \[ A = \pi r^2 \] The ratio of the areas of the two circles will be the square of the ratio of their radii: \[ \frac{A_1}{A_2} = \left(\frac{r_1}{r_2}\right)^2 = \left(\frac{3}{2}\right)^2 = \frac{9}{4} \]
Step 3: Conclusion.
Thus, the ratio of the areas of the two circles is \( 9:4 \). The correct answer is (B).