Question

The diameter of a semi circular protractor is 14cm, then find its perimeter.

Answer 1

Hint: Circumference of a circle is \[2\pi r\] where r is the radius of the circle. And in this case as it is a semi circle the formula for the circumference of its arc is \[\pi r\] . Use these to find the perimeter of the required region.

Complete Step by Step Solution:
We know that the circumference of a circle is \[2\pi r\]
Therefore the circumference of semi-circle will be \[\dfrac{{2\pi r}}{2} = \pi r\]
Now the perimeter of the whole protractor will be
 Circumference of the semicircle + Diameter of the Protractor
Diameter of the protractor is already given as 14cm
Let us try to find the Circumference of the semicircle
As nothing is mentioned in the question regarding \[\pi \]
Let us take it as \[\pi = \dfrac{{22}}{7}\]
Taking this value of \[\pi \] , We can get the circumference as
\[\begin{array}{l}
 = \pi r\\
 = \dfrac{{22}}{7} \times 7\\
 = 22cm
\end{array}\]
Now as we have all the values
Let us try to find the perimeter of the Protractor \[ = (22 + 14) = 36cm\]
Therefore the answer is 36cm.

Note: The radius of the circle is half of the diameter i.e., if d is the diameter and r is radius then \[r = \dfrac{d}{2}\]. Many of the students make the mistake of just finding the circumference of the semicircle after which they forgot to add the diameter but as a protractor is a closed figure the diameter is also a part of its perimeter. Therefore it must be added.