Question

If the diameter of a semicircular protractor is 14cm then find its perimeter.
A.36cm
B.76cm
C.112cm
D.162cm

Answer 1

Hint: Perimeter is the length of the outline of the shape, and in case of the circle it is known as circumference represented as \[\pi d\], where $d$ is the diameter of the circle. Since the given protractor is a semi-circle, then the circumference of semicircle becomes the half of the circumference of the circle given as \[P = \dfrac{{\pi d}}{2}\] or as \[P = \pi r\]and this is added by the base length of the protractor which is the diameter length in case of perimeter.

Complete step-by-step answer:
Given the diameter of the semicircular protractor is \[d = 14cm\]
Hence the radius of the protractor will be \[r = \dfrac{d}{2} = \dfrac{{14}}{2} = 7cm\]

To find the perimeter of the protractor we need to add the circumference length of the protractor with the base length which is the diameter, hence the perimeter will be
\[P = \dfrac{{\pi d}}{2} + d\]
Now substitute the values in the equation we get
 \[
  P = \dfrac{{\pi d}}{2} + d \\
   = \dfrac{{22}}{7} \times \dfrac{{14}}{2} + 14 \\
 \]
By further solving we get
\[
  P = \dfrac{{22}}{7} \times \dfrac{{14}}{2} + 14 \\
   = 22 + 14 \\
   = 36cm \\
 \]
Hence the perimeter of the protractor will be\[ = 36cm\]
So, the correct answer is “Option A”.

Note: We can find the perimeter of a figure only when it is a close region. Here the diameter makes the figure a closed region, so the perimeter was found. Perimeter is the total length of the outer boundary hence it needs to be closed.