A piece of wire 144 cm long is bent to form a semicircle. Find the diameter of the semicircle in metres.

Given:

A piece of wire 144 cm long is bent to form a semicircle.

To do:

We have to find the diameter of the semicircle in metres.

Solution:

When the given piece of the wire is converted into a semicircle, its circumference is equal to the length of the wire.

This implies,

Circumference of the semi-circle $= 144\ cm$

We know that,

Circumference of a semi-circle of diameter $d= (\frac{1}{2}\pi d ) + d$

Let the diameter of the semi-circle formed be $d$.

Therefore,

$(\frac{1}{2}\pi d ) + d= 144\ cm$

$(\frac{1}{2} \times \frac{22}{7} +1 ) d=144\ cm

$(\frac{11}{7}+1)d = 144\ cm$

$(\frac{11+7}{7})d = 144\ cm$

$\frac{18}{7}d=144\ cm$

$d = 144 \times \frac{7}{18}\ cm$

$d=8\times7\ cm$

$d = 56\ cm$

$d = 56 \times ( \frac{1}{100})\ m$

$d = \frac{56}{100}\ m$

$d=0.56\ m$

The diameter of the semi-circle is $0.56\ m$.

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Updated on: 10-Oct-2022

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