Question

The wire of length 144cm bent to form a semicircle region. find its radius​

Answer 1

Step-by-step explanation:

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

========================

From the properties of circle, we know : -

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

=======================

Hence,

⇒ ( 1 / 2 πd + d ) = 144 cm

\implies d \bigg\{ \bigg( \dfrac{1}{2} \times \dfrac{22}{7} \bigg) + 1\bigg\}=144\:cm⟹d{(

2

1

×

7

22

)+1}=144cm

= > d( 11 / 7 + 1 ) = 144 cm

= > d x 18 / 7 = 144 cm

= > d = 144 cm x 7 / 18

= > d = 56 cm

= > d = 56 x ( 1 / 100 ) m

= > d = 0.56 m

Hence,

Diameter of the semi - circle is 0.56 m or 56 cm.

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