Question

Find the area of a semicircle with diameter $6cm$
$
  A)3.5\pi sq.units \\
  B)4.5\pi sq.units \\
  C)5.5\pi sq.units \\
  D)6.5\pi sq.units \\
$

Answer 1

Hint: Find the area of the complete circle and divide it by 2.
First, we are going to find the area of the whole complete circle, for that we need radius. Since, in the question we are given diameter, we can calculate radius from that and then we can calculate the area of the whole circle and then we divide the whole area by 2, so that we can obtain the area of the semi-circle.

Complete step by step solution:
 We are given that there is a semi-circle with the diameter of $6cm$
First, we have to calculate the radius from the diameter, which is half of it.
$r = \dfrac{d}{2}$$r = \dfrac{d}{2}$
So, the radius we get is $3cm$
Since, we have obtained the radius, now we can use it to find the area of the complete circle.
So, the formula for area of circle is
\[
  A = \dfrac{{9\pi }}{2} \\
   = 4.5\pi \\
 \]\[A = \pi {r^2}\]
On substituting the r value, we will get the area of the complete circle.
\[
  A = \pi {r^2} \\
   = \pi \times 3 \times 3 \\
   = 9\pi \\
\]
Since, we need only the area of the semi-circle, we need to divide it by 2.
Area of the semicircle is half the area of the circle.
So, \[A = \dfrac{{\pi {r^2}}}{2}\]

It means that
\[
  A = \dfrac{{9\pi }}{2} \\
   = 4.5\pi sq.units \\
\]
So, the correct answer is Option B.

Note: We need to understand the question well whether we have to find the area of the circle or the semi-circle. If we divide the area by four, we will get the area of the quarter portion of the circle. If it’s just the area of the circle, just substitute in the formula with no division.