Question

If the diameter of a semicircular protractor is 14 cm, then the perimeter of the protractor is:
(a) 26 cm
(b) 14 cm
(c) 28 cm
(d) 36 cm

Answer 1

Hint: The semicircular protractor is in the shape of a protractor, therefore we will use the formula of the perimeter of the semicircle to solve this question. The perimeter of the semicircle protractor is given by \[P=2r+\pi r,\] where r is the radius of the semicircle.

Complete step-by-step answer:
Given that the diameter of a semicircular protractor is 14 cm.
d = 14 cm.
Let the radius of the semicircle be r then we know that,
\[r=\dfrac{d}{2}\]
\[\Rightarrow r=\dfrac{14}{2}=7cm\]
We know that the perimeter of a semicircular protractor is given by:
\[\text{Perimeter of semicircle }=\dfrac{\text{Perimeter of circle}}{2}+\text{diameter of the circle}\]
We consider the diameter of the circle as the given shape is a semicircular protractor, i.e. the semicircle is enclosed with the line of length equal to the diameter.
\[\therefore \text{Perimeter }=\dfrac{2\pi r}{2}+d\]
\[\therefore \text{Perimeter }=\pi r+d\]
We know that, \[\pi =\dfrac{22}{7},r=7\text{ and }d=14\]
Substituting these values in the formula, we get,
\[\text{Perimeter }=\dfrac{22}{7}\times 7+14\]
\[\text{Perimeter }=22+14\]
Perimeter = 36 cm
Therefore, the perimeter of the semicircular protractor is 36 cm.
Hence, option (d) is the right answer.

Note: Students generally write the perimeter of the semicircle as half of that of an incorrect circle. In a semicircle, the boundary consists of half of the circle and the diameter. Hence, the diameter should also be added making the perimeter of semicircular protractor as
\[\text{Perimeter of semicircle }=\dfrac{\text{Perimeter of circle}}{2}+\text{diameter}\]