Question

The curves in the below image are perfect semicircles. If the straight line AB measures 18 units, what is the length of the curved line of the figure?

• A. 18𝜋
• B. 9𝜋
• C. 4.5𝜋
• D. 36𝜋

Answer 1

The correct option is B 9𝜋

$\text{Let}AC=x\Rightarrow CB=18-x$
The length of the curved line is equal to the sum of the perimeters of the two semi-circles.
Perimeter of a semi-circle = $\frac{\pi \times diameter}{2}$
Perimeter of the semi-circle with diameter AC = $\frac{\pi x}{2}$
Perimeter of the semi-circle with diameter CB = $\frac{\pi (18-x)}{2}$
$\therefore \text{Length of the curved line}=\frac{\pi x}{2}+\frac{\pi (18-x)}{2}$
$=\frac{\pi x+\pi (18-x)}{2}$
$=\frac{\pi x+18\pi -\pi x)}{2}$
$=9\pi \text{units}$