Question

The perimeter of the semicircular protractor is 72cm. then its radius is?

Answer 1

Hint: The question is related to the circle. We must know the formula of the perimeter of a circle that is $2\pi r$ and for the semi-circle, we have to divide the perimeter of the circle by 2. So, the perimeter of the semicircular protractor is $\pi r$.

Complete step-by-step answer:
Given that the perimeter of the semicircular protractor is 72 cm
We have to find the radius of the circle
The perimeter of the semi-circle = $\pi r + 2r$
Putting the value of perimeter of the semi-circle
$72cm = \pi r + 2r$
Taking the r as common on the left-hand side
$ \Rightarrow 72cm = r(\pi + 2)$
Put the value of pie
$ \Rightarrow 72cm = r(\dfrac{{22}}{7} + 2)$
Solving the left-hand side
\[ \Rightarrow 72cm = r(\dfrac{{22 + 14}}{7})\]
Adding the numbers in the numerator of the left-hand side
$ \Rightarrow 72cm = r(\dfrac{{36}}{7})$
Equating both sides
$ \Rightarrow 72 \times \dfrac{7}{{36}}cm = r$
Cancel the numerator and denominator part of the fraction on the right-hand side
$\therefore r = 14cm$

Hence, the radius of the circle is 14 cm.

Note: You must know the formula of the perimeter of a semi-circle protector that is $\pi r + 2r$. Always write cm and m at the end of the number because the radius and perimeter are measured in cm and m.