Perimeter of semicircular protractor = 72 cm
The formula of the perimeter of semicircle = πr + 2r, where r is the radius
According to the question,
πr + 2r = 72 cm
⇒ r(π + 2) = 72 cm
Putting the value of π as 3.14 in the sum,
⇒ r(3.14 + 2) = 72 cm
⇒ 5.14 r = 72 cm
⇒ r = \(\frac{72}{5.14}cm\)
⇒ r = 14.007 cm
We know, Diameter = 2r, where r is the radius.
∴ Diameter = 2r
= (2 × 14.007) cm
= 28.014 cm
The diameter of the semicircle protractor is 28.014 cm.
