The ratio of the numbers giving the measure of the circumference and the area of a circle of radius 3 cm is

Options

A. `1:3`
B. `2:3`
C. `2:9`
D. `3:2`

Answer

To find the ratio of the circumference and the area of a circle with a radius of 3 cm, we can follow these steps:

### Step 1: Calculate the Circumference of the Circle
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
Substituting the radius \( r = 3 \) cm into the formula:
\[ C = 2 \pi (3) = 6 \pi \text{ cm} \]

### Step 2: Calculate the Area of the Circle
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
Substituting the radius \( r = 3 \) cm into the formula:
\[ A = \pi (3)^2 = 9 \pi \text{ cm}^2 \]

### Step 3: Form the Ratio of Circumference to Area
Now, we need to find the ratio of the circumference to the area:
\[ \text{Ratio} = \frac{C}{A} = \frac{6 \pi}{9 \pi} \]
Here, we can simplify the ratio by canceling out \( \pi \):
\[ \text{Ratio} = \frac{6}{9} = \frac{2}{3} \]

### Final Answer
The ratio of the numbers giving the measure of the circumference and the area of the circle is:
\[ \frac{2}{3} \]

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