To find the area of a sector of a circle, you can use the formula:
\[ A = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \( A \) is the area of the sector,
- \( \theta \) is the angle of the sector in degrees,
- \( r \) is the radius of the circle.
Given:
- \( \theta = 216^\circ \)
- \( r = 7 \) inches
Now, plug in the values into the formula:
\[ A = \frac{216}{360} \times \pi (7)^2 \]
First, calculate \( (7)^2 \):
\[ (7)^2 = 49 \]
Now, substitute that back into the equation:
\[ A = \frac{216}{360} \times \pi \times 49 \]
Next, simplify \( \frac{216}{360} \):
\[ \frac{216}{360} = \frac{3}{5} \]
Now substitute that in:
\[ A = \frac{3}{5} \times \pi \times 49 \]
Now multiply:
\[ A = \frac{3 \times 49}{5} \pi = \frac{147}{5} \pi \]
This can be expressed as a decimal:
\[ \frac{147}{5} = 29.4 \]
Thus, the area of the sector is:
\[ A = 29.4\pi \text{ in}^2 \]
The correct response is:
A = 29.4π in²
1 answer