Question

The central angle of a semicircle is:
A. ${90}^{\circ }$
B. ${270}^{\circ }$
C. ${180}^{\circ }$
D. ${360}^{\circ }$

Answer 1

Hint: For solving this question you should know about the figure and area of a semicircle. A complete circle contains two semicircles in it. And we can prove it by an example. And then we can also find that the central angle of a semicircle is exactly half of the centre of a circle. So, for this we will prove the half area.

Complete step by step answer:
According to our question it is asked of us to find the central angle of a semicircle. So, if we take a circle with a radius of 7m and we see the diagram for this, then:

The circle’s centre is a point where the angle is ${360}^{\circ }$. But if we see a semicircle, then:

Here the centre is on a straight line and the angle on any point of a straight line is always ${180}^{\circ }$. So, the angle is ${180}^{\circ }$. And if we look for the areas of semicircle and circle, then:
It is given that the radius of the circle is 7m. So, we know that the area of a circle is calculated by $\pi r^2$.
Thus the area of a whole circle is:
$\begin{array}{rl}& A=\pi {\left(7\right)}^2\\ & \Rightarrow A=49\pi \\ & \Rightarrow A=49\times {\displaystyle \frac{22}{7}}\\ & \Rightarrow A=154m^2\end{array}$
So, the area of the whole circle is $154m^2$.
We know that, to calculate the area of a semicircle, it is half of the whole circle. So, we can calculate it by the formula ${\displaystyle \frac{1}{2}}\pi r^2$. The radius for the semicircle is 7m.
So, the area of the semicircle is:
$\begin{array}{rl}& A^{\prime }={\displaystyle \frac{1}{2}}\pi r^2\\ & \Rightarrow A^{\prime }={\displaystyle \frac{1}{2}}\times \pi \times {\left(7\right)}^2\\ & \Rightarrow A^{\prime }=77m^2\end{array}$
So, the area of the semicircle is exactly half of the whole circle and it is $77m^2$.
So, the correct answer is “Option C”.

Note: The area of a semicircle is half the area of a circle of the same radius and a circle contains two semicircles in its area. We can directly do half of the complete area of the circle to calculate the area of a semicircle. And it is mandatory that the area will be of the same radius circle and semicircle of same radius.