If area of quadrant of a circle is `154cm^2`, then find its radius. `(use pi=22/7)`

Options

A. 7
B. 49
C. 14
D. 28

Answer

To find the radius of a circle given that the area of a quadrant of the circle is 154 cm², we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Area of a Quadrant**:
The area of a quadrant of a circle is one-fourth of the area of the entire circle. Therefore, if the area of the quadrant is given as 154 cm², we can express this mathematically as:
\[ \text{Area of quadrant} = \frac{1}{4} \times \text{Area of circle} \]

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

3. **Relate the Area of Quadrant to the Radius**:
Since the area of the quadrant is one-fourth of the area of the circle, we can write:
\[ 154 = \frac{1}{4} \times \pi R^2 \]
Substituting \( \pi = \frac{22}{7} \):
\[ 154 = \frac{1}{4} \times \frac{22}{7} R^2 \]

4. **Multiply Both Sides by 4**:
To eliminate the fraction, multiply both sides by 4:
\[ 4 \times 154 = \frac{22}{7} R^2 \]
\[ 616 = \frac{22}{7} R^2 \]

5. **Multiply Both Sides by 7**:
To further eliminate the fraction, multiply both sides by 7:
\[ 616 \times 7 = 22 R^2 \]
\[ 4312 = 22 R^2 \]

6. **Divide Both Sides by 22**:
Now, divide both sides by 22 to solve for \( R^2 \):
\[ R^2 = \frac{4312}{22} \]
\[ R^2 = 196 \]

7. **Take the Square Root**:
Finally, take the square root of both sides to find \( R \):
\[ R = \sqrt{196} = 14 \text{ cm} \]

### Final Answer:
The radius of the circle is \( 14 \text{ cm} \).