Area of a Sector of a Circle

Area of a sector is given by

\left(\dfrac{\theta}{360^o}\right)\times \pi r^2

Sector of a Circle

A circle sector/ sector of a circle is defined as the region of a circle enclosed by an arc and two radii.

The smaller area is called the minor sector and the larger area is called the major sector.

FiguresAreaPerimeter 
Circle This image has an empty alt attribute; its file name is image-54.png \pi r^2 or \dfrac{\pi d^2}{4}   2\pi or  \pi dr : radius
d : diameter
 \pi=\dfrac{22}{7}\ or\ 3.14 
Semicircle This image has an empty alt attribute; its file name is image-55.png \dfrac{\pi r^2}{2}  \pi r+2r  
Quadrant This image has an empty alt attribute; its file name is image-56.png  \dfrac{\pi r^2}{4}   \dfrac{\pi r}{2}+2r 
Ring This image has an empty alt attribute; its file name is image-57.png \pi(R+r)\ (R-r)  2\pi R (Outer circumference ) 2\pi r (Inner circumference) R : Radius of bigger circle
r : Radius of smaller circle
Sector This image has an empty alt attribute; its file name is image-58.png(i) \dfrac{\theta}{360}\times \pi r^2

(ii)  \dfrac{1}{2}lr
 \dfrac{\theta}{360}\times2\pi r+2r  r : Radius of circle
l : length of arc
Segment This image has an empty alt attribute; its file name is image-59.png \dfrac{\theta}{360}\pi r^2-\dfrac{1}{2}r^2\sin\theta  \dfrac{\pi r\theta}{180}+2r\sin\dfrac{\theta}{2}   \theta : angle subtended by arc at centre

Example

If a pizza is cut in such a way that it divides into 8 equal parts as shown in the figure, then what is the area of each piece of the pizza? The radius of the circle shaped pizza is 7 cm.

Solution

Area of  1 piece =\dfrac{1}{8} of area of circle

=\dfrac{1}{8}\times \pi r^2

=\dfrac{1}{8}\times\dfrac{22}{7}\times7\times7

=\dfrac{77}{4}\ \mathrm{cm^2}

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