Question

A wire of length 36 cm is bent in the form of a semicircle. What is the radius of the semicircle?

• A. $9cm$
• B. $8cm$
• C. $7cm$
• D. $6cm$

Answer 1

Answer: (C)

$7cm$

Length of wire is in the form of semicircle.

Given, length of wire $=36cm$

The length of the wire will cover the diameter as well as the circumference of the semicircle.

$\therefore$Length of the wire $=\frac{1}{2}\left(2\pi r\right)+2r$
$\Rightarrow 36=(\pi +2)r$
$\Rightarrow 36=(\frac{22}{7}+2)r=\frac{36}{7}\times r$
$\Rightarrow r=7cm$.

Hence, the radius of the semicircle is $7cm$.