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:
$\frac{50}{\pi} mm$
B:
$\frac{\pi}{50} mm$
C:
$\frac{25\pi}{2} mm$
D:
$25mm$

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Answer 1

Answer:

$(\text{A})\:\frac{50}{\pi}\:\text{mm}$

Step-by-step explanation:

This the arc is 90 degrees and there are 360 degrees in a circle, it makes up $\frac{90}{360}=\frac{1}{4}$ of the circle. Therefore, its length will be $\frac{1}{4}$ 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:

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