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