A sector of a circle has the area of 12 cm squared. If the angle at the centre is 60 degrees, calculate the diameter of the circle.

Question

The answer I got was $45.8$cm but it seems wrong. I did

$$ A=\pi r^2 $$

$$ 12= \frac{60}{360} \pi r^2 $$

$$ \frac{12}{\pi} \cdot \frac{360}{60}=r=22.9183118 $$

$$ d=45.8 $$

Answer 1

Assuming that I've accurately transcribed your approach, your error is that you didn't take the square root. You should have $r = \sqrt{\frac{72}{\pi}} \doteq 4.7873$, and then $d \doteq 9.5746$.

Answer 2

Between the second and third line you lost the square on $r$, so did not take a square root that you should have.