Can someone confirm my answer for finding the radius when given theta in radians and the area and the area of a sector of a circle?

Question

So the problem is:

$A$ denotes the area of the sector of a circle of radius $r$ formed by the central angle $\theta$. Find the missing quantity and round the answer to $3$ decimal places. $$\theta= \frac{1}{4}\text{radian},$$ $$ A= 6 \text{ cm}^2,$$ $$r=?$$

I got $r= 6.928$ cm.

Is my math correct?

Answer 1

We have the area of a sector of radius $r $ and angle subtended at the centre, $\theta $ (in radians) as: $$A =\frac { \pi r^2}{2\pi}\theta = \frac {\theta r^2}{2} $$

In our question, $A=6$ and $\theta = \frac {1}{4} $. Thus, $$r = \sqrt {\frac {2A}{\theta}} = \sqrt {12 \times 4} $$ $$\boxed {r = 6.928 \text { cm }} $$ Your answer is thus correct. Hope it helps.