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# The area of a circle is 314sq.cm and area of its minor sector is 31.4sq.cm. find the area of its major sector.A. $282.6c{m^2}$B. $200.6c{m^2}$C. $180.04c{m^{^2}}$D. $1220.09c{m^2}$

Answer Verified
Hint: As the question mentions, we have the area of the circle and the area of its minor sector and we have to find the area of its major sector. We know that a circle is made up by its major and minor sector.

Complete step-by-step answer:
A circle sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger area as the major sector
The area of the circle = the area of its minor sector + the area of its major sector …. (1)
Simply put the values of area of circle and its sector
Area of circle is 314sq.cm
Area of its minor sector is 31.4sq.cm
Area of its major sector?
Putting the values in (1)
$314 = 31.4 +$area of its major sector
By evaluating the equation
Area of its major sector $= 314 - 31.4$
Area of its major sector $= 282.6$
So, the area of major sector of a circle is 282.6sq.cm
Hence the option A is the correct option

Note: Area of circle = Area of major sector + Area of minor sector.
A sector is the area bounded by two radii of the circle. If the angle is less than 180, then it is called a minor sector. The angle for the major sector is more than 180.