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 its quadrant is 154 cm², we can follow these steps:

### Step 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. The formula for the area of a circle is given by:
\[ \text{Area of Circle} = \pi r^2 \]
Thus, the area of a quadrant is:
\[ \text{Area of Quadrant} = \frac{1}{4} \pi r^2 \]

### Step 2: Set up the equation
According to the problem, the area of the quadrant is 154 cm². Therefore, we can write:
\[ \frac{1}{4} \pi r^2 = 154 \]

### Step 3: Substitute the value of π
We are given that \(\pi = \frac{22}{7}\). Substituting this into the equation gives:
\[ \frac{1}{4} \left(\frac{22}{7}\right) r^2 = 154 \]

### Step 4: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 4:
\[ \left(\frac{22}{7}\right) r^2 = 154 \times 4 \]
Calculating the right side:
\[ 154 \times 4 = 616 \]
So, we have:
\[ \frac{22}{7} r^2 = 616 \]

### Step 5: Solve for \(r^2\)
Next, we can multiply both sides by \(\frac{7}{22}\) to isolate \(r^2\):
\[ r^2 = 616 \times \frac{7}{22} \]

### Step 6: Simplify the right side
Calculating \(616 \times \frac{7}{22}\):
First, simplify \(\frac{616}{22}\):
\[ 616 \div 22 = 28 \]
Now, multiply by 7:
\[ r^2 = 28 \times 7 = 196 \]

### Step 7: Find the radius \(r\)
To find \(r\), take the square root of \(r^2\):
\[ r = \sqrt{196} = 14 \text{ cm} \]

### Final Answer
Thus, the radius of the circle is:
\[ \boxed{14 \text{ cm}} \]