Find the area of a ring shaped region enclosed between two concentric circles of radii 20 cm and 15 cm.

Answer

To find the area of the ring-shaped region enclosed between two concentric circles with radii 20 cm and 15 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Radii**:
- The radius of the outer circle (R) is 20 cm.
- The radius of the inner circle (r) is 15 cm.

2. **Formula for the Area of a Circle**:
- The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]

3. **Calculate the Area of the Outer Circle**:
- Using the radius of the outer circle (R = 20 cm):
\[ A_{outer} = \pi (20)^2 = \pi \times 400 = 400\pi \text{ cm}^2 \]

4. **Calculate the Area of the Inner Circle**:
- Using the radius of the inner circle (r = 15 cm):
\[ A_{inner} = \pi (15)^2 = \pi \times 225 = 225\pi \text{ cm}^2 \]

5. **Find the Area of the Ring-Shaped Region**:
- The area of the ring-shaped region is the difference between the area of the outer circle and the area of the inner circle:
\[ A_{ring} = A_{outer} - A_{inner} = 400\pi - 225\pi = (400 - 225)\pi = 175\pi \text{ cm}^2 \]

6. **Substitute the Value of \(\pi\)**:
- Using \(\pi \approx \frac{22}{7}\):
\[ A_{ring} = 175 \times \frac{22}{7} \text{ cm}^2 \]

7. **Calculate the Final Area**:
- Simplifying:
\[ A_{ring} = \frac{175 \times 22}{7} = \frac{3850}{7} \approx 550 \text{ cm}^2 \]

### Final Answer:
The area of the ring-shaped region is approximately **550 cm²**.