Question

In the area of a circle is $38.5{m^2} $, and then find the circumference.
A) 22
B) 2.2
C) 38.5
D) 3.85

Answer 1

Hint: We have given area of a circle. Formula of area of circle is $\pi {r^2} $. So, with the help of this we will find radius r.
Then find the circumference of a circle by using radius r.

Complete step-by-step answer:
We have given the area of a circle.
Area of a circle$ = 38.5{m^2} $
$ \Rightarrow \pi {r^2} = 38.5$
$\pi $ is the mathematical constant and its value is $\dfrac{{22}}{7}$ .
$ \Rightarrow \dfrac{{22}}{7}{r^2} = 38.5$
To find radius r, divide both sides by$\dfrac{{22}}{7}$.
After dividing, it will be multiplied by its reciprocal.
$ \Rightarrow \dfrac{7}{{22}} \times \dfrac{{22}}{7}{r^2} = 38.5 \times \dfrac{7}{{22}}$
Simplify it.
$ \Rightarrow {r^2} = 12.25$
Find the square root of both sides.
$ \Rightarrow r = 3.5$
So, radius is the 3.5m
               

Circumference of a circle $ = 2\pi r$
Substitute all the values.
Circumference of a circle $ = 2 \times \dfrac{{22}}{7} \times 3.5$
Simplify it
$ \Rightarrow \dfrac{{154}}{7}$
$ \Rightarrow 22$
Hence the circumference is 22m.

So, the correct answer is “Option A”.

Note: When radius is given in the cm then the unit of area of a circle should be $c {m^2} $ & circumference is cm.
When radius is given in meters then the area of a circle is in the ${m^2}$ & circumference is m.