The radii of two concentric circles are 19 cm and 16 cm respectively. The area of the ring enclosed by these circles is

Options

A. `320cm^(2)`
B. `330cm^(2)`
C. `332cm^(2)`
D. `340cm^(2)`

Explanation

To find the area of the ring enclosed by two concentric circles with radii of 19 cm and 16 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Radii:**
- The radius of the outer circle (R) = 19 cm
- The radius of the inner circle (r) = 16 cm

2. **Calculate the Area of the Outer Circle:**
- The formula for the area of a circle is given by:
\[ \text{Area} = \pi R^2 \]
- Substituting the radius of the outer circle:
\[ \text{Area of outer circle} = \pi \times (19)^2 = \pi \times 361 \]

3. **Calculate the Area of the Inner Circle:**
- Using the same formula for the inner circle:
\[ \text{Area of inner circle} = \pi r^2 = \pi \times (16)^2 = \pi \times 256 \]

4. **Find the Area of the Ring:**
- The area of the ring is the difference between the area of the outer circle and the area of the inner circle:
\[ \text{Area of the ring} = \text{Area of outer circle} - \text{Area of inner circle} \]
- Substituting the areas calculated:
\[ \text{Area of the ring} = \pi \times 361 - \pi \times 256 \]
- Factor out \(\pi\):
\[ \text{Area of the ring} = \pi \times (361 - 256) = \pi \times 105 \]

5. **Calculate the Numerical Value:**
- Using \(\pi \approx \frac{22}{7}\):
\[ \text{Area of the ring} = \frac{22}{7} \times 105 \]
- Performing the multiplication:
\[ = \frac{22 \times 105}{7} = \frac{2310}{7} = 330 \text{ cm}^2 \]

### Final Answer:
The area of the ring enclosed by the two concentric circles is **330 cm²**.