Question

What is the formula to find the perimeter of a semicircle with radius r?
A) $\pi r$
B) $2\pi r$
C) $r\left( \pi +2\right) $
D) $2\left( \pi +r\right) $

Answer 1

Hint: In this question it is given that we have to find the formula to find the perimeter of a semicircle with radius r. So first of all we have to draw the diagram,

As we know that the perimeter of the above shape is the length of the boundary i.e, length of ABCOA, so to find the perimeter of the semi circle, we have to know the circumference of the circle of radius r.

Complete step-by-step solution:
As we know that the circumference of the above circle is $2\pi r$ which we can also call as the perimeter of the circle, where r is the radius.
Now, as we know that semicircle is the half portion of the circle, so the perimeter of the circular segment of semicircle is $$\dfrac{2\pi r}{2}$$=$\pi r$.
So from the diagram we can say that the length of circular segment ABC=$\pi r$.
And the length of $AC=AO+OC=r+r=2r$
Therefore, the perimeter of semicircle ABCO = Circular segment ABC + AC$$=\pi r+2r=r\left( \pi +2\right) $$
Hence the correct option is option C.
Note: A perimeter is a path that surrounds a two-dimensional shape, It can be thought of as the length of the outline of a shape. Also you need to know that circumference of a circle is the length of its circular boundary, so that is why we used the term circumference as a perimeter in the solution.