Question

complete the proportion to find the area of the shaded sector:

\frac{210^{\circ}}{360^{\circ}} = \frac{a}{324\pi}

find the area of the shaded sector. write your answers using pi with no spaces.

\text{area}_{\text{sector}} = 189\pi \text{ units}^2

Explanation:

Calculate total circle area

$$ \text{Area}_{\text{total}} = \pi r^2 = \pi (18)^2 = 324\pi $$

Set up the sector area proportion

$$ \frac{210^{\circ}}{360^{\circ}} = \frac{A}{324\pi} $$

Solve for the shaded sector area

$$ A = \frac{210}{360} \times 324\pi = \frac{7}{12} \times 324\pi = 189\pi $$

Answer:

Question 1

Complete the proportion to find the area of the shaded sector:
\(\frac{\text{210}}{360^{\circ}} = \frac{A}{\text{324\pi}}\)

Question 2

Find the area of the shaded sector. Write your answers using 'pi' with no spaces.
\(\text{Area}_{\text{sector}} =\) <blank>\(189\text{pi}\)</blank> \(\text{units}^2\)