Question

1. determine the arc length of $widehat{tw}$. give your answer in terms of $pi$

arc length = ________

1. determine the sector area of the shaded region qop. give your answer in terms of $pi$

sector area = ________

Explanation:

(Problem 9):

Step1: Recall arc length formula

Arc length: $s = \frac{\theta}{360^\circ} \times 2\pi r$

Step2: Substitute values ($\theta=135^\circ, r=24$ ft)

$s = \frac{135^\circ}{360^\circ} \times 2\pi \times 24$

Step3: Simplify the expression

$s = \frac{3}{8} \times 48\pi = 18\pi$

(Problem 10):

Step1: Find shaded sector angle

Total circle is $360^\circ$, subtract $90^\circ$: $\theta = 360^\circ - 90^\circ = 270^\circ$

Step2: Recall sector area formula

Sector area: $A = \frac{\theta}{360^\circ} \times \pi r^2$

Step3: Substitute values ($\theta=270^\circ, r=4$ in)

$A = \frac{270^\circ}{360^\circ} \times \pi \times 4^2$

Step4: Simplify the expression

$A = \frac{3}{4} \times 16\pi = 12\pi$

Answer:

1. Arc Length = $18\pi$ ft
2. Sector Area = $12\pi$ square inches