Question

Find the circumference of a circle whose area is \[1386c{m^2}\]
A) \[132c{m^2}\]
B) \[132cm\]
C) \[42cm\]
D) \[21c{m^2}\]

Answer 1

Hint: Here we will first use the formula of area of a circle to get the value of radius of the circle and then we will use the formula for circumference of the circle and substitute the value of radius in that formula to get the desired value.
The area of the circle is given by:-
\[area = \pi {r^2}\] where r is the radius of the circle.
The circumference of the circle is given by:-
\[C = 2\pi r\] where r is the radius of the circle.

Complete step-by-step answer:
It is given that area of the circle is \[1386c{m^2}\]
Now we know that the area of the circle is given by:-
\[area = \pi {r^2}\] where r is the radius of the circle.
We will use the value of \[\pi = \dfrac{{22}}{7}\]
Hence putting in the respective values we get:-
$\Rightarrow$\[1386 = \dfrac{{22}}{7} \times {r^2}\]
Solving it further we get:-
$\Rightarrow$\[{r^2} = 63 \times 7\]
Taking square root of both the sides we get:-
$\Rightarrow$\[\sqrt {{r^2}} = \sqrt {63 \times 7} \]
Solving it further we get:-
$\Rightarrow$\[r = 21cm\]
Hence we got the radius as 21 cm.
Now we know that the circumference of the circle is given by:-
\[C = 2\pi r\] where r is the radius of the circle.
Hence, putting \[\pi = \dfrac{{22}}{7}\] and the value of radius we get:-
$\Rightarrow$\[C = 2 \times \dfrac{{22}}{7} \times 21\]
Solving it further we get:-
$\Rightarrow$\[C = 2 \times 22 \times 3\]
Simplifying it further we get:-
$\Rightarrow$\[C = 132cm\]
Hence, we got the circumference of the circle as 132 cm.

Therefore, option B is the correct option.

Note: Students should note that the circumference of the circle is the perimeter made by the closed figure i.e. circle. Also, since the unit of perimeter is units like centimeter, meters so the circumference also has the units as cm or m.