Question

The ratio between the diameters of two circles is \( 4 : 9 \). The ratio between their circumferences will be:

• A. \( 9 : 4 \)
• B. \( 4 : 9 \)
• C. \( 2 : 3 \)
• D. \( 4 : 5 \)

Hint:

The circumference of a circle is directly proportional to its diameter, so the ratio of their circumferences will be the same as the ratio of their diameters.

Answer 1

The Correct Option is B

Step 1: Understanding the relationship between diameter and circumference.
The circumference \( C \) of a circle is given by the formula: \[ C = \pi \times d \] where \( d \) is the diameter of the circle.
Step 2: Using the ratio of diameters.
The ratio between the diameters of two circles is given as \( 4 : 9 \). Since the circumference of a circle is directly proportional to its diameter (i.e., if \( d_1 \) and \( d_2 \) are the diameters, then \( C_1 = \pi \times d_1 \) and \( C_2 = \pi \times d_2 \)), the ratio of the circumferences will be the same as the ratio of the diameters.
Step 3: Conclusion.
Therefore, the ratio between the circumferences of the two circles will also be \( 4 : 9 \).