Find the area of a quadrant of a circle whose radius is 14 cm.

Explanation

To find the area of a quadrant of a circle with a radius of 14 cm, we can follow these steps:

### Step 1: Identify the radius
Let the radius \( r \) of the circle be given as:
\[ r = 14 \, \text{cm} \]

**Hint:** Remember that the radius is the distance from the center of the circle to any point on its circumference.

### Step 2: Calculate the area of the full circle
The formula for the area \( A \) of a circle is:
\[ A = \pi r^2 \]

Substituting the value of \( r \):
\[ A = \pi (14)^2 \]
\[ A = \pi \times 196 \]

**Hint:** Use the value of \( \pi \) as \( \frac{22}{7} \) for easier calculations.

### Step 3: Substitute the value of \( \pi \)
Now, substituting \( \pi \) into the area formula:
\[ A = \frac{22}{7} \times 196 \]

**Hint:** You can simplify \( 196 \) as \( 28 \times 7 \).

### Step 4: Simplify the area calculation
\[ A = \frac{22}{7} \times (28 \times 7) \]
The \( 7 \) in the numerator and denominator cancels out:
\[ A = 22 \times 28 \]

**Hint:** Break down \( 22 \times 28 \) into smaller multiplications if needed.

### Step 5: Calculate \( 22 \times 28 \)
Calculating:
\[ 22 \times 28 = 616 \, \text{cm}^2 \]

**Hint:** You can also use the distributive property: \( 22 \times (20 + 8) = 440 + 176 \).

### Step 6: Find the area of the quadrant
Since a quadrant is one-fourth of the circle, we divide the area of the circle by 4:
\[ \text{Area of the quadrant} = \frac{616}{4} \]

**Hint:** Dividing by 4 can be done by halving twice.

### Step 7: Calculate the area of the quadrant
\[ \text{Area of the quadrant} = 154 \, \text{cm}^2 \]

### Final Answer
The area of the quadrant of the circle is:
\[ \boxed{154 \, \text{cm}^2} \]