When the circumference of a toy ballon is increased from 20 cm to 25 cm, its radius (in cm) is increased by :

Options

A. 5
B. `(5)/(pi)`
C. `(5)/(2pi)`
D. `(pi)/(5)`

Answer

To solve the problem, we need to find the increase in the radius of the balloon when its circumference changes from 20 cm to 25 cm.

### Step-by-Step Solution:

1. **Understand the formula for circumference**:
The formula for the circumference (C) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

2. **Calculate the initial radius**:
When the circumference is 20 cm:
\[ 20 = 2\pi r_1 \]
To find \( r_1 \):
\[ r_1 = \frac{20}{2\pi} = \frac{10}{\pi} \text{ cm} \]

3. **Calculate the new radius**:
When the circumference is increased to 25 cm:
\[ 25 = 2\pi r_2 \]
To find \( r_2 \):
\[ r_2 = \frac{25}{2\pi} = \frac{12.5}{\pi} \text{ cm} \]

4. **Find the increase in radius**:
The increase in radius is:
\[ \Delta r = r_2 - r_1 \]
Substituting the values we found:
\[ \Delta r = \frac{12.5}{\pi} - \frac{10}{\pi} = \frac{12.5 - 10}{\pi} = \frac{2.5}{\pi} \text{ cm} \]

5. **Approximate the increase**:
Using \( \pi \approx 3.14 \):
\[ \Delta r \approx \frac{2.5}{3.14} \approx 0.796 \text{ cm} \]

### Final Answer:
The radius of the balloon is increased by approximately \( 0.796 \) cm.