Question

find the area of the sector. leave your answer in terms of pi.
18 cm
270°
243π
\\(\frac{9}{10}\\)π
\\(\frac{27}{2}\\)π
338π

Explanation:

Step1: Recall sector area formula

The formula for the area of a sector is $\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle and $r$ is the radius.

Step2: Substitute given values

Here, $\theta = 270^\circ$ and $r = 18$ cm.
$\text{Area} = \frac{270^\circ}{360^\circ} \times \pi \times (18)^2$

Step3: Simplify the fraction and calculate

Simplify $\frac{270}{360} = \frac{3}{4}$, and $(18)^2 = 324$.
$\text{Area} = \frac{3}{4} \times \pi \times 324 = 3 \times 81 \times \pi = 243\pi$

Answer:

243$\pi$