Question

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

\frac{\box}{360^{\circ}} = \frac{a}{\pi (\box)^2}

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

\text{area}_{\text{sector}} = \box \text{ units}^2

Explanation:

Set up the sector area proportion

$$ \frac{210^{\circ}}{360^{\circ}} = \frac{A}{\pi \cdot 18^2} $$

Calculate the total area of the circle

$$ \text{Area}_{\text{circle}} = \pi \cdot 18^2 = 324\pi $$

Solve for the shaded sector area

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

Answer:

Question 1

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

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

Question 2

Find the area of the shaded sector. Write your answers using 'pi' with no spaces:

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