Question

A protractor is a semi-circle of radius 6.1cm. Calculate the perimeter of a protractor?

Answer 1

Hint: The perimeter of a circle is also known as the circumference of the circle. The perimeter of a protractor is the sum of the diameter and half of the circumference of the circle. Representing the entire question diagrammatically gives us a better understanding of the question. The circumference of the circle is $2\pi r$ which is the length of the boundary of the circle.

Complete step-by-step answer:
Let’s draw a diagram to represent the entire question.
                                                                                                                                              

The above diagram represents a protractor which is a semicircle where:
Radius = r = 6.1cm
AB is the diameter and O is the center.
The perimeter = half the circumference of the circle with the same radius + diameter
Half of the circumference of the circle with same radius = $\dfrac{1}{2} \times 2\pi r$
Diameter = $2r$
Therefore, the perimeter = $(\dfrac{1}{2} \times 2\pi r) + (2r)$
$=(\dfrac{1}{2} \times 2\pi (6.1)) + (2 \times 6.1)$
By substituting the value of $\pi $, we get:
$=(\dfrac{1}{2} \times 2 \times \dfrac{{22}}{7} \times 6.1) + (2 \times 6.1)$
$=19.17 + 12.2$
$=31.37cm$
The perimeter of the protractor is 31.37cm.

Note: When figures like square, rectangle, triangle are given, the sum of the length of all sides is called the perimeter, when a curve is present like a circle’s outline or an arc, then it’s called the circumference where we use $\pi $in the formula whose approximate value is 3.14 The value of the radius is given in centimeters. We have to be careful and check the given units of the parameters and the units of the solution.