A solid lead ball of radius 6 cm is melted and then drawn into a wire of diameter 0.2 cm. Find the length of the wire.
Answers
Answer:
Length of wire is 28800 cm
Step-by-step explanation:
Vol of ball=Vol of wire
4/3*pi*r^3 = pi*r^2*h
4/3*216 = 0.01*h
4*72 = 0.01*h
288/0.01 = h
h = 28800cm
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Given:
- Radius of solid lead ball = 6 cm
- Diameter of wire = 0.2 cm
To find out:
Find the length of the wire.
Formula used:
- Volume of sphere = 4/3 πr³
- Volume of cylinder = πr²h
Solution:
We have,
Radius of the lead ball = 6 cm
Therefore,
Volume of lead ball = 4/3 πr³
= 4/3 × 22/7 × 6³
= 4/3 × 22/7 × 216
= 19008/21 cm³
The wire is a cylinder of radius = 0.1 cm
Let the length of the wire be h cm .
Then,
Volume of wire = πr²h
= 22/7 × ( 0.1 )² × h
= 11h/350 cm³
But,
Volume of the wire = Volume of the lead ball
➠ 11h/350 = 19008/21
➠ h = 19008/21 × 350/11 cm
➠ h = 19008 × 350/21 × 11 × 100
➠ h = 288 m
Hence, the length of wire is 288 m .