A piece of wire 144 cm long is
bent to form a semicircle as
shown in the figure. Find the
diameter of the semicircle, giving
your answer in metres. (Take it to be
22
7
Answers
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
========================
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.