Question

The area of a circle is 38.5 cm². The circumference of the circle is
(a) 6.2 cm
(b) 12.1 cm
(c) 11 cm
(d) 22 cm

Answer 1

(d) 22 cm
Let the radius be r cm.
We know:
Area of a circle$=\mathrm{\pi }{r}^2{\text{cm}}^2$
Thus, we have:
$\mathrm{\pi }{r}^2=38.5$
$$\begin{gathered} \Rightarrow \frac{22}{7}\times r^2=38.5 \\ \Rightarrow r^2=\left(38.5\times \frac{7}{22}\right) \\ \Rightarrow r^2=\left(\frac{385}{10}\times \frac{7}{22}\right) \\ \Rightarrow r^2=\frac{49}{4} \\ \Rightarrow r=\frac{7}{2} \end{gathered}$$
Now,
Circumference of the circle$=2\mathrm{\pi }r$
$$\begin{gathered} =2\times \frac{22}{7}\times r \\ =\left(2\times \frac{22}{7}\times \frac{7}{2}\right) \\ =22\text{cm} \end{gathered}$$