Sector Area and Arc Length

In the diagram of circle O, what is the area, in terms of  $\pi$  , of the shaded region?

•  $\frac{4\pi}{3}$  

•  $\frac{20\pi}{3}$  

•  $\frac{32\pi}{3}$  

•  $\frac{160\pi}{3}$  

Tags

CCSS.HSG.C.B.5

CCSS.HSG.GMD.A.1

In the diagram of circle O, the area of the shaded sector AOC is   $12\pi\ in^2$  and the length of OA is 6 inches. Determine the  $m<AOC$ .

•  $140\degree$  

•  $120\degree$  

•  $100\degree$  

•  $80\degree$  

Tags

CCSS.HSG.C.B.5

CCSS.HSG.C.A.2

The area of sector  in the following image is  $28\pi$ . Find the measurement of the central angle labeled  $x\degree$ .

•  $42\degree$  

•  $70\degree$  

•  $86\degree$  

•  $140\degree$  

Tags

CCSS.HSG.C.B.5

In circle O, diameter , chord , and radius  are drawn, and the measure of arc BC is 108°. Some students wrote these formulas to find the area of sector COB. Which students wrote correct formulas?

Sam:  $\frac{3}{10}\cdot\pi\cdot\left(BC\right)^2$  
Amanda:  $\frac{108}{360}\cdot\pi\cdot\left(OC\right)^2$  
Jia:  $\frac{3}{10}\cdot\pi\cdot\left(\frac{1}{2}OB\right)^2$  
Zoha:  $\frac{108}{360}\cdot\pi\cdot\left(\frac{1}{2}AB\right)^2$  

• Sam and Zoha

• Amanda and Jia
  

• Jia and Sam

• Zoha and Amanda

Find the exact arc length in terms of  $\pi$ ,  of a circle with radius of 4 cm and central angle of  $225\degree$ .

•  $\frac{5\pi}{2}$  

•  $5\pi$  

•  $10\pi$  

•  $40\pi$  

Tags

CCSS.HSG.C.B.5

CCSS.HSF.TF.A.1

Find the arc length. Leave your answer in terms of π.

• $\frac{7}{4}\pi$

• $\frac{7}{2}\pi$

• $\frac{1}{8}\pi$

• $45\pi$

Find the length of the bold arc. Leave your answer in terms of  $\pi$  

•  $5688\pi\ ft$  

•  $\frac{95}{6}\pi\ ft$  

•  $\frac{752}{5}\pi\ ft$ 

•  $\frac{1805}{12}\pi\ ft$  

Find the arc length of the bolded arc. Give your answer in terms of π.

• $\frac{65\pi}{12}\ cm$

• 17.02 cm

• $\frac{845\pi}{24}cm$

• 26π cm

A circle is drawn to represent a pizza with a 12 inch diameter. The circle is cut into eight congruent pieces. What is the length of the outer edge of any one piece of this circle? (HINT: If the circle is cut into 8 congruent pieces, how many degrees would each slice account for?) 

•  $\frac{3\pi}{4}$  

•  $\pi$  

•  $\frac{3\pi}{2}$  

•  $3\pi$  

In circle O, the radius is 4, and the length of minor arc AB is 4.2 feet. Find the measure of minor arc AB to the nearest degree. (HINT: minor arc AB is equal to <AOB)

• 90

• 60

• 55

• 113