   Question Answers

# Formula to find the area of the quadrant of a circle is:A.$\pi {{r}^{2}}$ B.$\dfrac{\pi {{r}^{2}}}{2}$ C.$\dfrac{\pi {{r}^{2}}}{4}$ D.$\dfrac{\pi {{r}^{2}}}{8}$  Hint: The given problem is related to the area of a circle. The area of a sector of a circle, having radius $r$, which subtends an angle $\theta$ at the centre is given as $\left( \dfrac{\theta }{2\pi } \right)\times \pi {{r}^{2}}$ . The angle subtended by the quadrant of a circle at the centre is $\dfrac{\pi }{2}$ .

Before we proceed with the solution, we must understand the sector of a circle. The sector of a circle is defined as the region enclosed between two radii and the arc of the circle. If the angle between the radii is $\theta$ , then $\theta$ is called the central angle. The region corresponding to the smaller central angle is called the minor sector and the region corresponding to the larger central angle is called the major sector. If $\theta =\dfrac{\pi }{2}$ , then the sector is called a quadrant. Consider the figure. In the figure $\alpha <\beta$ . So, the sector corresponding to angle $\alpha$ is the minor sector and the sector corresponding to angle $\beta$ is the major sector.
Now, the area of a sector of a circle, having radius $r$ , which subtends an angle $\theta$ at the centre is given as $\left( \dfrac{\theta }{2\pi } \right)\times \pi {{r}^{2}}$ . We know the angle subtended by the quadrant of a circle at the centre is $\dfrac{\pi }{2}$ . So, the area of the quadrant will be equal to $\dfrac{\dfrac{\pi }{2}}{2\pi }\times \pi {{r}^{2}}=\dfrac{\pi }{4\pi }\pi {{r}^{2}}=\dfrac{\pi {{r}^{2}}}{4}$ .
Hence, the area of the quadrant of a circle having radius $r$ is equal to $\dfrac{\pi {{r}^{2}}}{4}$ .
Hence, option B. is the correct option.

Note: Most of the students get confused between sector and segment. Sector is the region between two radii and the circular arc, whereas segment is the region between a chord and its corresponding arc.

Area of a Sector of a Circle Formula  Area of a Rhombus Formula  To Find the Weight of a Given Body Using Parallelogram Law of Vectors  Surface Area of a Prism Formula  How to Find Square Root of a Number  Area of Triangle Formula  Area of Square Formula  Area of Equilateral Triangle Formula  The Making of a Scientist  Changing the Period of a Pendulum  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 9 - What Happened to The Reptiles  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 1 - A Tale of Two Birds  Important Questions for CBSE Class 9 Science Chapter 4 - Structure of The Atom  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 8 - A Pact with the Sun  Important Questions for CBSE Class 9 Science Chapter 5 - The Fundamental Unit of Life  CBSE Class 8 Science Reaching The Age of Adolescence Worksheets  Important Questions for CBSE Class 8 Social Science Our Past 3 Chapter 9 - The Making of the National Movement: 1870s -1947  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 6 - The Monkey and the Crocodile  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 2 - The Friendly Mongoose  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 3 - The Shepherd's Treasure  CBSE Class 10 Hindi A Question Paper 2020  Hindi A Class 10 CBSE Question Paper 2009  Hindi A Class 10 CBSE Question Paper 2015  Hindi A Class 10 CBSE Question Paper 2016  Hindi A Class 10 CBSE Question Paper 2012  Hindi A Class 10 CBSE Question Paper 2010  Hindi A Class 10 CBSE Question Paper 2007  Hindi A Class 10 CBSE Question Paper 2013  Hindi A Class 10 CBSE Question Paper 2008  Hindi A Class 10 CBSE Question Paper 2014  NCERT Solutions for Class 9 English Beehive Chapter 5 - A Legend of The Northland  RD Sharma Solutions for Class 9 Maths Chapter 21 - Surface Area and Volume of a Sphere  RS Aggarwal Class 8 Mathematics Solutions for Chapter-18 Area of a Trapezium and a Polygon  RD Sharma Solutions for Class 9 Maths Chapter 19 - Surface Area and Volume of A Right Circular Cylinder  RD Sharma Solutions for Class 9 Maths Chapter 18 - Surface Area and Volume of a Cuboid and Cube  RD Sharma Solutions for Class 9 Maths Chapter 20 - Surface Area and Volume of A Right Circular Cone  RS Aggarwal Class 11 Solutions Chapter-16 Conditional Identities Involving the Angles of a Triangle  RS Aggarwal Solutions Class 8 Chapter-18 Area of a Trapezium and a Polygon (Ex 18B) Exercise 18.2  NCERT Solutions for Class 9 English Beehive Chapter 9 - The Bond of Love  Lakhmir Singh Chemistry Class 9 Solutions Chapter 4 - Structure Of The Atom  