Question

If the perimeter of a semi-circular protractor is $66$cm. Find the diameter of the protractor.

(Take $\pi =\frac{22}{7}$).

• A. $\frac{77}{3}$ cm
• B. $\frac{7}{3}$ m
• C. $\frac{1}{3}$ m
• D. $\frac{16}{3}$ cm

Answer 1

Answer: (A)

$\frac{77}{3}$ cm

Let the radius of the protractor be $r$ cm.
Then, Perimeter$=66cm$
$\Rightarrow \pi r+2r=66$
$\Rightarrow r[\frac{22}{7}+2]=66$
$\Rightarrow r\left(\frac{36}{7}\right)=66$
$\Rightarrow r=\frac{66\times 7}{36}$
$\Rightarrow r=\frac{77}{6}$
$\therefore$ Diameter $=2r=\frac{77}{3}$