Question

1. determine the arc length of $widehat{tv}$. give your answer in terms of $pi$$\frac{135}{360} cdot 2pi24$arc length = ________10. determine the sector area of the shaded region qop. give your answer in terms of $pi$sector area = ________

Explanation:

Step1: Identify arc length formula

Arc Length = $\frac{\theta}{360^\circ} \times 2\pi r$, where $\theta=135^\circ$, $r=24$ ft

Step2: Substitute values and simplify

$\frac{135}{360} \times 2\pi \times 24 = \frac{3}{8} \times 48\pi = 18\pi$
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Step3: Identify shaded sector angle

Total circle = $360^\circ$, right angle = $90^\circ$, so shaded $\theta=360^\circ-90^\circ=270^\circ$, $r=4$ in

Step4: Use sector area formula

Sector Area = $\frac{\theta}{360^\circ} \times \pi r^2$

Step5: Substitute values and simplify

$\frac{270}{360} \times \pi \times 4^2 = \frac{3}{4} \times 16\pi = 12\pi$

Answer:

Arc Length = $18\pi$ ft
Sector Area = $12\pi$ in$^2$