The circumference of a circle exceeds its diameter by 270 cm. Find its diameter.

Answer

To solve the problem where the circumference of a circle exceeds its diameter by 270 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the relationship between circumference and diameter**:
- We know that the circumference (C) of a circle is given by the formula:
\[ C = \pi D \]
where \(D\) is the diameter of the circle.
- According to the problem, the circumference exceeds the diameter by 270 cm:
\[ C = D + 270 \]

2. **Setting up the equation**:
- From the two equations we have:
\[ \pi D = D + 270 \]

3. **Rearranging the equation**:
- We can rearrange the equation to isolate terms involving \(D\):
\[ \pi D - D = 270 \]
- Factoring out \(D\):
\[ D(\pi - 1) = 270 \]

4. **Substituting the value of \(\pi\)**:
- We can use the approximation \(\pi \approx \frac{22}{7}\):
\[ D\left(\frac{22}{7} - 1\right) = 270 \]
- Simplifying \(\frac{22}{7} - 1\):
\[ \frac{22}{7} - \frac{7}{7} = \frac{15}{7} \]
- Therefore, our equation becomes:
\[ D \cdot \frac{15}{7} = 270 \]

5. **Solving for \(D\)**:
- To find \(D\), multiply both sides by the reciprocal of \(\frac{15}{7}\):
\[ D = 270 \cdot \frac{7}{15} \]
- Calculating \(D\):
\[ D = \frac{270 \cdot 7}{15} \]
- Simplifying \(270 \div 15 = 18\):
\[ D = 18 \cdot 7 = 126 \text{ cm} \]

6. **Final answer**:
- The diameter of the circle is:
\[ D = 126 \text{ cm} \]