Question

If the perimeter of a semi-circular protractor is 108 cm, find the diameter of the protractor (Take $\pi =\frac{22}{7}$).

Answer 1

Let the radius of the protractor be r cm. Then,
Perimeter $=108cm.$

$\Rightarrow \frac{1}{2}\left(2\pi r\right)$ + $2r$ $=$ $108$ ..........$[\therefore Perimeterofasemicircle=\frac{1}{2}(2\pi r\left)\right]$

$\Rightarrow \pi r+2r=108\Rightarrow \frac{22}{7}\times r+2r=108\Rightarrow 36r=108\times 7\Rightarrow r=3\times 7=21$

$\therefore$ Diameter of the protractor $=2r=$ $(2\times 21)cm=42cm$