The area of a circle is 38.5 cm2. The circumference of the circle is

`
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 $=2 \pi r$

$=2 \times \frac{22}{7} \times r$

$=\left(2 \times \frac{22}{7} \times \frac{7}{2}\right)$

 

$=22 \mathrm{~cm}$

 

Leave a comment