Question

a piece of wire is 144 cm long is bent to form a semicircle .Find diameter of semicircle​

Answer 1

It is given that the total length of the piece of wire is 144 cm, which can't be changed.

Thus, if the piece of wire is converted into a semicircle, its circumference can't be changed.

Hence,

= > Circumference of semi-circle = 144 cm

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From the properties of circle, we know : -

Circumference of semi-circle = ( 1 / 2 πd ) + d

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$⇒( \frac{1}{2} \pi \times d + d) = 144 \\ \\ ⇒d( \frac{1}{2} \pi \: + 1) = 144 \\ \\ ⇒d( (\frac{1}{2} \times \frac{22}{7}) + 1) = 144 \\ \\⇒ d( \frac{11}{7} + 1) = 144 \\ \\ ⇒ \frac{18}{7} d = 144 \\ \\ ⇒d = 56 \: cm \: or \: 0.56 \: m \\ \\ \\ \\ \underline{\boxed{\sf{diameter \: of \: circle = 56 \: cm \: or \: 0.56 \: m }}}$