Question

A wire is in the form of semi – circle of 7cm radius. The length of the wire will be: -
(a) 22cm
(b) 36cm
(c) 5cm
(d) 39cm

Answer 1

Hint: Draw a rough diagram of the semi – circle and find its perimeter which will be the sum of its diameter and circumference. Assume the radius as ‘r’ and apply the relation: - Perimeter of semi – circle = \[\pi r+2r\]. Substitute the given value of r and \[\pi =\dfrac{22}{7}\] to get the answer.

Complete step-by-step answer:
Here, we have been provided with a wire which is in the form of a semi – circle of radius 7cm. We have to find the length of the wire. So, let us draw a rough diagram of a semi – circle.

In the above figure we have assumed the radius of the semi – circle as ‘r’. Clearly, we can see that the semi – circle contains half of the circumference of a circle and a diameter. So, the total length of the wire will be the sum of both these components. Therefore, we have,
\[\Rightarrow \] Circumference of a complete circle = \[2\pi r\]
\[\Rightarrow \] Circumference of a semi – circle = \[\dfrac{2\pi r}{2}=\pi r\]
Now, perimeter of the wire = perimeter of the semi – circle
\[\Rightarrow \] Perimeter of the wire = \[2r+\pi r\]
\[\Rightarrow \] Perimeter of the wire = \[r\left( 2+\pi \right)\]
Substituting the value of r = 7cm and \[\pi =\dfrac{22}{7}\], we get,
\[\Rightarrow \] Perimeter of the wire = \[7\times \left( 2+\dfrac{22}{7} \right)\]
\[\Rightarrow \] Perimeter of the wire = 36cm
Therefore, the total length of the wire will be 36cm.

So, the correct answer is “Option (b)”.

Note: One must draw the figure of the semi – circle before solving the question otherwise we will get confused in the expression for the perimeter of the semi – circle. Here, we have to consider both the circumference and diameter of the semi – circle and not only its curved length, i.e. the circumference. You may see that we have substituted \[\pi =\dfrac{22}{7}\] because the radius of the semi – circle is 7cm and therefore it will get cancelled and our calculation will become easy.