A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding :
Major sector

Answer

To find the area of the major sector of a circle with a radius of 10 cm that subtends a right angle (90 degrees) at the center, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the radius and angle**:
- Given the radius \( r = 10 \) cm.
- The angle subtended at the center \( \theta = 90^\circ \).

2. **Calculate the area of the entire circle**:
- The formula for the area of a circle is:
\[ \text{Area} = \pi r^2 \]
- Substituting the radius:
\[ \text{Area} = \pi (10)^2 = 100\pi \text{ cm}^2 \]

3. **Calculate the area of the minor sector**:
- The area of the sector corresponding to the angle \( \theta \) is given by:
\[ \text{Area of sector} = \frac{\theta}{360^\circ} \times \text{Area of circle} \]
- Substituting the values:
\[ \text{Area of minor sector} = \frac{90}{360} \times 100\pi = \frac{1}{4} \times 100\pi = 25\pi \text{ cm}^2 \]

4. **Calculate the area of the major sector**:
- The area of the major sector is the area of the circle minus the area of the minor sector:
\[ \text{Area of major sector} = \text{Area of circle} - \text{Area of minor sector} \]
- Substituting the areas:
\[ \text{Area of major sector} = 100\pi - 25\pi = 75\pi \text{ cm}^2 \]

5. **Calculate the numerical value**:
- Using \( \pi \approx 3.14 \):
\[ \text{Area of major sector} \approx 75 \times 3.14 = 235.5 \text{ cm}^2 \]

### Final Answer:
The area of the major sector is approximately \( 235.5 \text{ cm}^2 \).

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