Arc Length, Arc Measure, Circumference

If the circumference of a circle is  $12\pi\ cm$ , then the arc length of a semicircle for this circle must be:

Hint:   $arc\ length=\frac{arc\ measure\times circumference}{360\degree\ or\ 2\pi\ radians}$  
Note that we use either $360\degree$ or $2\pi\ radians$ in the denominator of the formula depending on the units given for the problem.  The arc measure of any semicircle is  $180\degree.$ 

•  $24\pi\ cm$  

•  $24\pi\ cm^2$  

•  $6\pi\ cm$  

•  $6\pi\ cm^2$  

•  $6\ cm$  

Tags

CCSS.HSG.C.B.5

If the circumference of a circle is  $10\ ft$ , then the arc length of a minor arc which measures  $90\degree$ is:  

Hint:   $arc\ length=\frac{arc\ measure\ \times circumference}{360\degree\ or\ 2\pi\ radians}$  
Note that we use either $360\degree$ or  $2\pi\ radians$ in the denominator depending on the units given for the problem.  A  $90\degree$ arc represents $\frac{1}{4}$ of the entire circle.

•  $20\ ft$  

•  $5\ ft^2$  

•  $5\ ft$  

•  $2.5\ ft$  

•  $2.5\ ft^2$  

Tags

CCSS.HSG.C.B.5

If the circumference of a circle is  $3\pi\ cm$ , then the arc length of a minor arc measuring  $120\degree$ must be:

Hint:  A minor arc measuring  $120\degree$ represents  $\frac{1}{3}$ of the entire circle.  
 $arc\ length=\frac{arc\ measure\times circumference}{360\degree\ or\ 2\pi\ radians}$  
Note that we use either  $360\degree$ or  $2\pi\ radians$ in the denominator depending on the given units for the problem.

•  $9\pi\ cm$  

•  $9\pi\ cm^2$  

•  $1\ cm$  

•  $\pi\ cm^2$  

•  $\pi\ cm$  

Tags

CCSS.HSG.C.B.5

If a circle has a circumference of  $18\pi\ ft$ , then the arc length of a major arc measuring  $\frac{4\pi}{3}radians$ must be:

Hint:   $arc\ length=\frac{arc\ measure\times circumference}{360\degree\ or\ 2\pi\ radians}$  
Note that we use either  $360\degree$ or  $2\pi\ radians$ depending on the given units for the problem.  If you find radians difficult, convert the given arc measure to degrees using the conversion ratio  $\frac{180\degree}{\pi\ radians}$  , then calculate the arc length.

•  $12\pi\ ft^2$  

•  $12\pi\ ft$  

•  $6\pi\ ft$  

•  $6\pi\ ft^2$  

•  $15\pi\ ft$  

Tags

CCSS.HSG.C.B.5

If the arc length for a minor arc measuring  $90\degree$ is  $5\ cm$ , then the circumference of the circle must be:

Hint:   $circumference=\frac{arc\ length\times360\degree}{arc\ measure}$  
A  $90\degree$  arc represents $\frac{1}{4}$ of the entire circle.

•  $1.25\ cm$  

•  $10\ cm$  

•  $20\ cm^2$  

•  $20\ cm$  

•  $10\ cm^2$  

Tags

CCSS.HSG.C.B.5

If a circle with a circumference of   $24\pi\ cm$ has a minor arc with an arc length of $4\pi$ , then the arc measure for the minor arc must be:

Hint:   $arc\ measure=\frac{arc\ length\times360\degree}{circumference}$   

•  $60\degree$  

•  $30\degree$  

•  $90\degree$  

•  $55\degree$  

•  $65\degree$  

Tags

CCSS.HSG.C.B.5

If a circle with a circumference of  $20\ ft$ has a minor arc which has an arc length of  $5\ ft$ , then the measure of that arc must be:

Hint:   $arc\ measure=\frac{arc\ length\times2\pi\ radians}{circumference}$  

•  $\frac{\pi}{6}radians$  

•  $\frac{\pi}{4}radians$  

•  $\frac{\pi}{3}radians$  

•  $\frac{\pi}{2}radians$  

•  $\frac{2\pi}{3}radians$  

Tags

CCSS.HSG.C.B.5