If angle of the sector is `60^(@)`, then find the area of sector if radius 6m

Answer

To find the area of a sector of a circle, we can use the formula:

\[ \text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]

where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle,
- \(\pi\) is a constant approximately equal to \(3.14\).

Given:
- \(\theta = 60^\circ\)
- \(r = 6 \, \text{m}\)

### Step 1: Substitute the values into the formula

\[ \text{Area of Sector} = \frac{60}{360} \times \pi \times (6)^2 \]

### Step 2: Simplify the fraction

\[ \frac{60}{360} = \frac{1}{6} \]

### Step 3: Calculate \(r^2\)

\[ (6)^2 = 36 \]

### Step 4: Substitute back into the formula

\[ \text{Area of Sector} = \frac{1}{6} \times \pi \times 36 \]

### Step 5: Multiply \(\pi\) with \(36\)

Using \(\pi \approx 3.14\):

\[ \text{Area of Sector} = \frac{1}{6} \times 3.14 \times 36 \]

### Step 6: Calculate \(3.14 \times 36\)

\[ 3.14 \times 36 = 113.04 \]

### Step 7: Divide by \(6\)

\[ \text{Area of Sector} = \frac{113.04}{6} \approx 18.84 \, \text{m}^2 \]

### Final Answer

The area of the sector is approximately \(18.84 \, \text{m}^2\).

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