Question

The circle with center O has a minor arc BSA with a length of

Answer 1

Answer:

D. $\frac{27\pi}{2}$ inches.

Step-by-step explanation:

We have been given that the circle with center O has a minor arc BSA with a length of $3\pi^{2}$ inches. The central angle is 40°.

To find the circumference of circle we will use formula:

$\frac{\text{Central angle}}{2\pi}=\frac{\text{Arc length}}{2\pi r}$, where $2\pi$= measure of 360 degrees in radians and $2\pi r$= circumference of circle.  

Let us convert measure of central angle into radians.                        

$40^{o}=\frac{40*\pi}{180} =\frac{2\pi}{9}$

Upon substituting our given value in the formula we will get,        

$\frac{\frac{2\pi}{9}}{2\pi}=\frac{\frac{3\pi}{2}}{2\pi r}$

$\frac{2\pi}{18\pi}=\frac{3\pi}{4\pi r}$    

$\frac{1}{9}=\frac{3}{4r}$      

Cross multiplying we will get,      

$4r=27$  

$r=\frac{27}{4}$

Hence, the radius of our circle is 27/4 inches.  

Since the circumference of circle is $2\pi r$. Upon substituting  $r=\frac{27}{4}$ we will get,

$2\pi r=2\pi* \frac{27}{4}=\frac{27\pi}{2}$

Therefore, circumference of our given circle will be $\frac{27\pi}{2}$ inches and option D is the correct choice.