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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 $0.56\ m$.