Find the area of a sector of a circle of radius 6 cm with a central angle of 60 degrees.

Step 1: Identify Given Values

We are given the radius of the circle, $r$, as 6 cm, and the central angle of the sector, $\theta$, as 60 degrees. These are the key values needed to calculate the area of the sector.

Step 2: Convert Angle to Radians (Optional but good practice)

While the formula for the area of a sector can use degrees, it's often good practice to convert the angle to radians, especially for other formulas involving arc length or angular velocity. To convert degrees to radians, we multiply by $\frac{\pi}{180^\circ}$.

Step 3: Apply Area of Sector Formula

The formula for the area of a sector when the angle is in degrees is given by $\frac{\theta}{360^\circ} \times \pi r^2$. This formula essentially calculates the fraction of the total circle's area that the sector occupies.

Step 4: Substitute Values and Calculate

Substitute the given values of $\theta = 60^\circ$ and $r = 6 \text{ cm}$ into the formula. Simplify the fraction $\frac{60}{360}$ to $\frac{1}{6}$ and calculate $6^2 = 36$. Finally, multiply these values to get the area.

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