Question

If the radius of a circle is 7cm, then the area of the semicircle is:
A. $77{{m}^{2}}$
B. $44{{m}^{2}}$
C. $88{{m}^{2}}$
D. $154{{m}^{2}}$

Answer 1

Hint: To solve this question we should know about the area of the circle and should also know that the area of a semicircle is half of the area of a circle with the same radius. The area consists of only half part, so we can say that a circle is made with two semicircles.

Complete step by step answer:
In our question, it is given that the radius of the circle is 7m. So, we know that the area of a circle is calculated by the formula $\pi {{r}^{2}}$. Thus the area of the whole circle is,
$\begin{align}
  & A=\pi {{\left( 7 \right)}^{2}} \\
 & \Rightarrow A=49\pi \\
 & \Rightarrow A=49\times \dfrac{22}{7} \\
 & \Rightarrow A=154{{m}^{2}} \\
\end{align}$
So, we get the area of the whole circle as $154{{m}^{2}}$.
Now, 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, $\dfrac{1}{2}\pi {{r}^{2}}$.
The radius for the semicircle is 7m.
So, the area of the semicircle is,
$\begin{align}
  & A'=\dfrac{1}{2}\pi {{r}^{2}} \\
 & \Rightarrow A'=\dfrac{1}{2}\pi {{\left( 7 \right)}^{2}} \\
 & \Rightarrow A'=77{{m}^{2}} \\
\end{align}$
So, the area of the semicircle is exactly half of the whole circle and it is $77{{m}^{2}}$.
So, the correct answer is “Option A”.

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