Question

Area of a quadrant is equal to:
A) $\dfrac{1}{2}$Area of the circle
B) $\dfrac{1}{4}$Area of the circle
C) $\dfrac{1}{8}$Area of the circle
D) None of these

Answer 1

Hint: We are given a quadrant and we have to find its area so for this we will understand that a circle is defined as the locus of all the points that are equidistant from the center now a quadrant is one fourth section of a circle which is obtained by a circle is divided evenly into four sections or rather $4$ quadrants by a set of two lines which are perpendicular to each other. Each of the four sections is called a quadrant when four such quadrants are joined; the structure that we get is nothing but a circle. Now to calculate the area of a quadrant divide the area of a circle by $4$ (as four quadrants make a circle).

Formula used:
Area of circle = $πr^2$
Where r is radius of circle

Complete step by step answer:
Step1: To calculate the area of a quadrant we will use the formula of area of circle as we know that quadrant is one fourth of a circle (as four quadrants make a circle)
Step2: The area is defined as the number of square units contained inside the circle that is π multiplied by the radius squared $r^2$. Therefore the area of a circle
$A$ = $πr^2$
To calculate the area of a quadrant divide the area of a circle by $4$ (as four quadrants make a circle) we get,
Area of quadrant=area of circle/4
Area$ = \dfrac{{\pi {r^2}}}{4}$
Area of quadrant$ = \dfrac{1}{4}\pi {r^2}$

Hence option (C) is the correct answer.

Note: In such types of questions students mainly get confused in understanding the terms quadrant before. They forget the meaning of quadrant here you can remember the meaning of quadrant by quad i.e. 4. Hence four parts makes one circle and they should remember that there is no any approach to solve this than to find the area of quadrant than to divide the area of the circle by $4$. Students get confused in the area of the circle and the area of the quadrant. Area of quadrant is one-fourth of area of circle as it forms central angle of ${90^0}$ while circle has central angle of ${360^0}$. Which is four times and these formulas don't depend on $\pi $ as it has a fixed value that is $\dfrac{{22}}{7}$ or $3.14$ it is a numerical constant.