Question

If the perimeter of a semicircular protractor is $36$ $cm$, then its diameter is

• A. $10$ $cm$
• B. $12$ $cm$
• C. $14$ $cm$
• D. $15$ $cm$

Answer 1

The correct option is C

$14$ $cm$

Calculate the diameter of a semi-circle

Given,

Perimeter of semicircular protractor $36$ $cm$

We know that,

The value of $\pi =\frac{22}{7}$

Step $1$:-

Let $r$ be the radius of the protractor.

$$\begin{gathered} \pi r+2r=36 \\ \Rightarrow r(\pi +2)=36 \\ \Rightarrow r\left(\frac{22}{7}+2\right)=36 \\ \Rightarrow r\left(\frac{22+14}{7}\right)=36 \\ \Rightarrow r\left(\frac{36}{7}\right)=36 \\ \Rightarrow r=\frac{36\times 7}{36} \\ \Rightarrow r=7 \end{gathered}$$

Radius of the protractor is $7$$cm$

Step $2$:-

Diameter of the protractor $=$$2\times r$

Diameter of the protractor $=$$2\times 7$

$=$$14$ $cm$

Hence, If the perimeter of a semicircular protractor is $36$ $cm$, then its diameter is $14$ $cm$.

Hence, option (C) is correct answer.