Question

A piece of wire 144 cm long is bent to form a semicircle. Find the diameter of the semicircle in metres. ps. the answer in my book is 0.56

Answer 1

Answer:

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

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

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From the properties of circle, we know : -

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

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Hence,

⇒ ( 1 / 2 πd + d ) = 144 cm

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

= > 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.

Answer 2

Answer:

Diameter of the semicircle in meters = 0.56m

Step-by-step explanation:

Given,

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

To find,

The diameter of the semicircle in meters.

Recall the formulas

The perimeter of a semicircle = πr + 2r

Diameter of the circle = 2r, where 'r' is the radius of the circle

Solution:

Since the wire is bent to form the semicircle,

The perimeter of the semicircle = length of the wire

πr + 2r = 144

r(π + 2) = 144

r($\frac{22}{7}+2$) = 144

r($\frac{22+14}{7}$) = 144

r ×$\frac{36}{7}$ = 144

r = $\frac{144 X 7 }{36}$

r = 28cm

Radius of the semicircle =  28cm

Diameter of the semicircle = 28 ×2 = 56cm

Diameter of the semicircle in meters = $\frac{56}{100}$m = 0.56m(1m = 100cm)

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