5. 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)
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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
(21 x7/22 )+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.
Answer:
answer 0.56
Step-by-step explanation:
- 144cm
- as we know:
- c = of semicircle
- = 1/2 π d × d
- 144 = 1/2 × 22/7 × d + d
- 144 = 11 d/ 7 + d
- taking a common
- 144 = d ( 11+7/7)
- taking l.c.m 9f 7 and 1
- 144 = d (11+1/7)
- 144 = 18d/7
- by cross-multiplication
- 144 ×7= 18d
- d=56m
- a.t.c
- convert cm into meter
- as we know
- 1m = 100cm
- 1cm=1/100m
- 56cm=56/100m
- diameter = 0.56m