Question

The circumference of a circle is 22 cm. Find the area of its one quadrant.

Answer 1

Hint:- We use the formula of the circumference of the circle to find out the radius. We will also use the fact that the circle is divided into four equal quadrants, after calculating the area of the circle by using the standard formula

Complete step-by-step answer:
It has been given that the circumference of a circle is 22 cm.
Let us assume that the radius of the circle is x cm
We know that the circumference of any circle of a given radius is $2\pi \left( {radius} \right)$
Thus, the circumference of the given circle is $2\pi x$cm
Equating this with the given value of the circumference, we get
$2\pi x = 22$
Now, let us take $\pi = \dfrac{{22}}{7}$
Therefore, we get
$2x \times \left( {\dfrac{{22}}{7}} \right) = 22$
On further simplification, we get
$x = \dfrac{7}{2}\;cm\;$
Thus, the radius of the given circle is $\dfrac{7}{2}\;cm\;$
We know that the area of a circle is given by $\pi {\left( {radius} \right)^2}$.
A circle can be equally divided into four equal quadrants. Hence, we can say that the area of any one of the quadrants is equal to one-fourth the total area of the circle.
Therefore, area of any one of the quadrants of the given circle is $\dfrac{{\pi {{\left( {radius} \right)}^2}}}{4}$
Replacing the value of the radius that we calculated earlier, we get the area of one of the quadrants as
$\dfrac{{\pi {{\left( x \right)}^2}}}{4}\;c{m^2}$
Thus, area is equal to $\dfrac{\pi }{4}{\left( {\dfrac{7}{2}} \right)^2}\;\;c{m^2}$
Taking $\pi = \dfrac{{22}}{7}$, we get the area as $\dfrac{{22}}{{4 \times 7}} \times \dfrac{{49}}{4}\;c{m^2}$

On further simplification, we get the area of any one of the quadrant as $9.625\;c{m^2}$

Note:- In such types of questions we will use the standard formulae of circumference and area of the circle. Quadrants are the four equal parts of a circle whose area is one-fourth the area of the circle.