Question
Answers

Find the area of a quadrant of a circle whose circumference is 22 cm.

Answer Verified Verified

Hint: First use circumference of the circle formula $2 \pi r$ to find the radius of the circle. Later divide the area of the circle formula by 4 to find the area of the quadrant since the quadrant of a circle is ${\dfrac{1}{4}^{th}}$ of the circle.


Complete step-by-step answer:

  Given, Circumference of the circle = 22 cm

 As we know that Circumference of the circle with radius ‘r’ is $2 \pi r$

  Taking $\pi = \dfrac{{22}}{7} $

   $\Rightarrow 2\pi r = 22 \Rightarrow r = \dfrac{{22}}{{2\pi }} = \dfrac{{22 \times 7}}{{2 \times 22}} = 3.5cm$

  Since, quadrant of a circle means ${\dfrac{1}{4}^{th}}$ of the circle 

 $ \therefore$ Area of quadrant of a circle =$ \dfrac{{{\text{Area of the circle}}}}{4}{\text{ = }}\dfrac{{\pi {r^2}}}{4}{\text{ = }}\dfrac{{22 \times {{\left( {3.5} \right)}^2}}}{{7 \times 4}} = 9.625{\text{ }}c{m^2} $

  Note - In these types of problems, a common parameter(which is radius here) between the given data(circumference) and the data which needs to be computed(area) is to be found using some formulas.


Bookmark added to your notes.
View Notes
×