Question

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

Answer 1

Hint:
we have given that the circumference of circle and we have to find the area of its quadrant
First, by using the formula of circumference of circle we will find the value of r
After that we get the area of the quadrant.

Complete step by step solution:
Here, we have given that the circumference of the circle is 22 cm.
So, we have to find the area of its quadrant
Let us assume the radius of the circle =r cm
 $\because $ circumference of circle =22cm
 $\because $ We know that circumference of circle $ = 2\pi r$
 $\therefore 2\pi r = 22$
 $\because \pi = \dfrac{{22}}{7}$
Now, put the value of $\pi $ in the above equation
 $\therefore 2 \times \dfrac{{22}}{7} \times r = 22$
$\therefore r = \dfrac{7}{2}$cm
Area of quadrant $ = \dfrac{{\pi {r^2}}}{4}$
$ = \dfrac{{22}}{7} \times \dfrac{1}{4} \times \dfrac{7}{2} \times \dfrac{7}{2}$
$ = \dfrac{{77}}{8}c{m^2}$

$\therefore $Area of quadrant $ = \dfrac{{77}}{8}c{m^2}$

Note:
Circumference of circle: Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas, the area of a circle defines the region occupied by it.
When we use the formula to calculate the circumference of the circle, then the radius of the circle is taken into account. Hence, we need to know the value of the radius or the diameter to evaluate the perimeter of the circle.
circumference of circle $ = 2\pi r$