Question

The area of a circle is $314$ square cm and the area of its minor sector is $31.4$ square cm. Find the area of its major sector.
A. $282.6$ cm$^2$
B. $200.6$ cm$^2$
C. $180.04$ cm$^2$
D. $1220.09$ cm$^2$

Answer 1

Hint: The circle is divided into two parts that are the major sector and the minor sector. The total area of a circle and the area of the minor sector are given.
We can find the area of the major sectors by subtracting the area of the minor sectors from the total area of a circle.
Area of Major sector = Total Area – Area of the minor sector

Complete step-by-step answer:
Consider the total area of a circle is $314$ square cm and the area of its minor sector is $31.4$ square cm.
Let the area of a major sector be $x$ square cm.
Total Area of circle= Area of Major sector + Area of minor sector
$314 = x + 31.4$
$ \Rightarrow x = 314 - 31.4$
$ \Rightarrow x = 282.6$ cm$^2$
The area of the major sector is $282.6$ cm$^2$.

Correct Answer: A. $282.6$ cm$^2$

Note:
Some formulas help to find areas of different shapes.
The Area of circle = $\pi {r^2}$,\[\;r\] is the radius of the circle.
The Area of square = ${a^2}$, $a$ is the side of the square.
The Area of rectangle= $l \times b$, $l$ is the length of the rectangle and $b$ is the breadth of the rectangle.