Find the area of sector of a circle with radius 4 cm and angle `60^@`.

Answer

To find the area of the sector of a circle with a radius of 4 cm and an angle of 60 degrees, we can follow these steps:

### Step 1: Understand the formula for the area of a sector
The area \( A \) of a sector of a circle can be calculated using the formula:
\[ A = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \( \theta \) is the angle of the sector in degrees,
- \( r \) is the radius of the circle.

### Step 2: Substitute the known values into the formula
In this case, the radius \( r = 4 \) cm and the angle \( \theta = 60^\circ \). Plugging these values into the formula gives:
\[ A = \frac{60}{360} \times \pi \times (4)^2 \]

### Step 3: Simplify the fraction
First, simplify \( \frac{60}{360} \):
\[ \frac{60}{360} = \frac{1}{6} \]
So the formula now looks like:
\[ A = \frac{1}{6} \times \pi \times (4)^2 \]

### Step 4: Calculate \( (4)^2 \)
Calculate \( (4)^2 \):
\[ (4)^2 = 16 \]
Now substitute this back into the area formula:
\[ A = \frac{1}{6} \times \pi \times 16 \]

### Step 5: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{1}{6} \times \frac{22}{7} \times 16 \]

### Step 6: Multiply the numbers
Now calculate:
\[ A = \frac{22 \times 16}{6 \times 7} \]
Calculating \( 22 \times 16 \):
\[ 22 \times 16 = 352 \]
So we have:
\[ A = \frac{352}{42} \]

### Step 7: Simplify the fraction
Now simplify \( \frac{352}{42} \):
\[ \frac{352 \div 2}{42 \div 2} = \frac{176}{21} \]

### Step 8: Calculate the final area
Now, we can calculate \( \frac{176}{21} \) to get a decimal value:
\[ \frac{176}{21} \approx 8.38 \text{ cm}^2 \]

### Final Answer
The area of the sector is approximately \( 8.38 \text{ cm}^2 \).

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