Question

PLS HELP!!!

A circle is subdivided by a central angle of 90 degrees. The length of the subtended arc is 25 mm. What is the radius of the circle?

A:

`(50)/(\pi) mm`
B:

`(\pi)/(50) mm`
C:

`(25\pi)/(2) mm`
D:

`25mm`

​

Answer 1

`(\text{A})\:(50)/(\pi)\:\text{mm}`

Explanation:

This the arc is 90 degrees and there are 360 degrees in a circle, it makes up
`(90)/(360)=(1)/(4)` of the circle. Therefore, its length will be
`(1)/(4)` of the circumference. Since its length is 25 mm, the circumference is then
`25\cdot 4=100\:\text{mm}`. The circumference of a circle is given by
`2\pi r`, where
`r` is the radius of the circle. Therefore, we can set up the following equation and solve for
`r`:

`2\pi r=100`

Solving, we get:

`2\pi r=100,\\\\r=(100)/(2\pi),\\\\r=\boxed{(\text{A})\:(50)/(\pi)\:\text{mm}}`.