Find the area of the sector of a circle with radius 5 cm and angle `60^@`.

Answer

To find the area of the sector of a circle with a radius of 5 cm and an angle of 60 degrees, we can follow these steps:

### Step 1: Identify the formula for the area of a sector
The formula for the area of a sector is given by:
\[ \text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \(\theta\) is the angle in degrees,
- \(r\) is the radius of the circle.

### Step 2: Substitute the given values into the formula
In this case, the radius \(r\) is 5 cm, and the angle \(\theta\) is 60 degrees. Substituting these values into the formula gives:
\[ \text{Area of sector} = \frac{60}{360} \times \pi \times (5)^2 \]

### Step 3: Simplify the fraction
Now, simplify \(\frac{60}{360}\):
\[ \frac{60}{360} = \frac{1}{6} \]
So the area of the sector becomes:
\[ \text{Area of sector} = \frac{1}{6} \times \pi \times (5)^2 \]

### Step 4: Calculate \(5^2\)
Calculating \(5^2\):
\[ 5^2 = 25 \]
Now substitute this back into the equation:
\[ \text{Area of sector} = \frac{1}{6} \times \pi \times 25 \]

### Step 5: Multiply the terms
Now, multiply the terms:
\[ \text{Area of sector} = \frac{25\pi}{6} \]

### Step 6: Approximate the value (if necessary)
If we want to approximate the value, we can use \(\pi \approx 3.14\):
\[ \text{Area of sector} \approx \frac{25 \times 3.14}{6} \approx \frac{78.5}{6} \approx 13.08 \text{ cm}^2 \]

### Final Answer
Thus, the area of the sector is:
\[ \text{Area of sector} = \frac{25\pi}{6} \text{ cm}^2 \quad \text{or approximately } 13.08 \text{ cm}^2 \]