Question

The angle of a sector of a circle with radius of 6 cm is $60^\circ$. The area of the sector will be:

• A. $36\pi\ \text{cm}^2$
• B. $12\pi\ \text{cm}^2$
• C. $6\pi\ \text{cm}^2$
• D. $132\ \text{cm}^2$

Hint:

For a sector, always multiply $\dfrac{\theta}{360}$ with the area of the circle $\pi r^2$. Double-check arithmetic to avoid mistakes.

Answer 1

The Correct Option is B

Step 1: Formula for area of a sector
\[ \text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]

Step 2: Substitute values
Here, $\theta = 60^\circ$, $r = 6$ cm.
\[ \text{Area} = \frac{60}{360} \times \pi \times 6^2 \] \[ = \frac{1}{6} \times \pi \times 36 = 6\pi\ \text{cm}^2 \]

Step 3: Verify carefully
Oops! Our result is $6\pi$ cm$^2$, not $12\pi$. Let's check options again:
Given options: $36\pi, 12\pi, 6\pi, 132$. Correct match is (C) $6\pi\ \text{cm}^2$.
\[ \boxed{\text{Area of sector} = 6\pi\ \text{cm}^2} \]