Question

Topic 8.4: Finding arc measures and lengths, and area of sectors within circlesFind the arc length and the area of the sector. Leave your answers in reduced fraction form,in terms of T. NO DECIMALSQ3.4.BeR3a. QR:3b. Area of sector:3c. mQR:9 cm120°CUS9 cm 45°AB4a. AB:4b. Area of sector:4c. mAB: I

Answer 1

Given:

`3)\theta=120^0,radius(r)=9cm`

To Determine: The length of the minor and the major arc and the area of the sector

`\begin{gathered} Length\text{ of an arc} \\ =(\theta)/(360^0)*2\pi r \\ 3)minorarclength=(120^0)/(360^0)*2\pi*9cm=6\pi cm \\ Area\text{ of sector=}(\theta)/(360^0)*\pi r^2=(120^0)/(360^0)*\pi(9cm)^2=27\pi cm^2 \\ majorarclength=2\pi r-6\pi=2\pi*9-6\pi=18\pi-6\pi=12\pi cm \end{gathered}`