Question

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

3π
2 inches. The central angle is 40°. What is the circumference of the circle?
A)
7π
2 inches
B)
9π
2 inches
C)
13π
2 inches
D)
27π
2 inches
The answer is D

Answer 1

D.
`(27\pi)/(2)` inches.

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)=(40*\pi)/(180) =(2\pi)/(9)`

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

`((2\pi)/(9))/(2\pi)=((3\pi)/(2))/(2\pi r)`

`(2\pi)/(18\pi)=(3\pi)/(4\pi r)`

`(1)/(9)=(3)/(4r)`

Cross multiplying we will get,

`4r=27`

`r=(27)/(4)`

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

Since the circumference of circle is
`2\pi r`. Upon substituting
`r=(27)/(4)` we will get,

`2\pi r=2\pi* (27)/(4)=(27\pi)/(2)`

Therefore, circumference of our given circle will be
`(27\pi)/(2)` inches and option D is the correct choice.