The problem involves finding the
area of a sector of a circle. Let's break it down step by step.
Step 1: Understand the given information
- The radius of the circle is given as \( r = 12 \, \text{cm} \).
- The central angle of the sector is \( \theta = 60^\circ \).
Step 2: Recall the formula for the area of a sector
The area \( A \) of a sector of a circle is given by:
\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]
where:
- \( \theta \) is the central angle in degrees,
- \( r \) is the radius of the circle,
- \( \pi \) is a constant (approximately \( 3.14159 \)).
Step 3: Substitute the given values into the formula
Here, \( \theta = 60^\circ \) and \( r = 12 \, \text{cm} \). Plugging these values into the formula:
\[
A = \frac{60^\circ}{360^\circ} \times \pi \times (12)^2
\]
Step 4: Simplify the fraction
\[
\frac{60^\circ}{360^\circ} = \frac{1}{6}
\]
So the formula becomes:
\[
A = \frac{1}{6} \times \pi \times (12)^2
\]
Step 5: Calculate \( (12)^2 \)
\[
(12)^2 = 144
\]
Thus:
\[
A = \frac{1}{6} \times \pi \times 144
\]
Step 6: Simplify the expression
\[
A = \frac{144}{6} \times \pi = 24 \pi
\]
Step 7: Write the final answer
The area of the sector is:
\[
\boxed{24\pi}
\]
If you need a numerical approximation, you can use \( \pi \approx 3.14159 \):
\[
A \approx 24 \times 3.14159 = 75.39822 \, \text{cm}^2
\]
However, the exact answer in terms of \( \pi \) is:
\[
\boxed{24\pi}
\]
Parent Tip: Review the logic above to help your child master the concept of geometry worksheet arc length sector area segment area answers.
