Question

Find the perimeter of the adjoined figure, which is semicircle, includes its diameter :

Answer 1

Hint: To find the perimeter of the figure we use the formula of the perimeter of semi-circle which is given as:
Perimeter of the semi-circle is: \[\left( \pi +2 \right)\dfrac{D}{2}\].
where D is the diameter of the figure.

Complete step by step solution:
Let us find the perimeter of the semi-circle and to find the perimeter of the semi-circle we use the formula of the semi-circle as:
Perimeter of the semi-circle is: \[\left( \pi +2 \right)\dfrac{D}{2}\]
According to the question given, the value of the diameter D is given as \[10\text{ }cm\]. Now placing the value of the diameter in the above formula as:
\[\Rightarrow \left( \pi +2 \right)\dfrac{10}{2}\]cm
Removing the bracket and multiplying the values of \[\dfrac{10}{2}\]to both \[\pi ,2\] we get the equation as:
\[\Rightarrow \left( \pi +2 \right)5\] cm
\[\Rightarrow 5\pi +10\] cm
Converting the value of the \[\pi \] into \[3.14\] and placing it in the above equation, we get the value of the perimeter is given as:
\[\Rightarrow 5\times 3.14+10\] cm
\[\Rightarrow 25.71\] cm
Therefore, the value of the perimeter of the semi-circle is given as \[25.71\] cm.

Note: The perimeter of the circle is given as \[\pi D\] and the perimeter of the semi-circle is actually divided into two parts with one part of the semicircle is the diameter line and the second part of the circle is the arc. Hence, the perimeter of the semicircle is equal to the sum of the perimeter of the arc and diameter of the semi-circle. Perimeter of the semi-circle = Perimeter of the arc + Perimeter of the diameter line.
\[\left( \pi +2 \right)r=\pi r+2r\]