# 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.$\dfrac{\pi {{r}^{2}}}{8}$

Last updated date: 25th Mar 2023

•

Total views: 306.3k

•

Views today: 3.83k

Answer

Verified

306.3k+ views

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 $\dfrac{\pi }{2}$ .

Complete step-by-step answer:

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.

Complete step-by-step answer:

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.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India