What will be the ratio of the circumference to the diameter of the circle if its original radius is tripled ?

Answer

To solve the question of what the ratio of the circumference to the diameter of a circle is when its original radius is tripled, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Original Radius**:
Let the original radius of the circle be \( r \).

2. **Calculate the Original Diameter**:
The diameter \( d \) of the circle is given by the formula:
\[ d = 2r \]

3. **Calculate the Original Circumference**:
The circumference \( C \) of the circle is given by the formula:
\[ C = 2\pi r \]

4. **Find the Ratio of Circumference to Diameter**:
Now, we need to find the ratio of the circumference to the diameter:
\[ \text{Ratio} = \frac{C}{d} = \frac{2\pi r}{2r} \]
Simplifying this gives:
\[ \text{Ratio} = \frac{2\pi r}{2r} = \frac{\pi}{1} = \pi \]

5. **Triple the Radius**:
If the radius is tripled, the new radius \( r' \) becomes:
\[ r' = 3r \]

6. **Calculate the New Diameter**:
The new diameter \( d' \) is:
\[ d' = 2r' = 2(3r) = 6r \]

7. **Calculate the New Circumference**:
The new circumference \( C' \) is:
\[ C' = 2\pi r' = 2\pi(3r) = 6\pi r \]

8. **Find the New Ratio of Circumference to Diameter**:
Now, we find the new ratio:
\[ \text{New Ratio} = \frac{C'}{d'} = \frac{6\pi r}{6r} \]
Simplifying this gives:
\[ \text{New Ratio} = \frac{6\pi r}{6r} = \frac{\pi}{1} = \pi \]

### Conclusion:
The ratio of the circumference to the diameter remains \( \pi \) even when the radius is tripled.