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Question
The diameter of a sphere is 6 cm. It is melted and drawn in to a wire of diameter 2 mm. The length of the wire is
Options
12 m
18 m
36 m
66 m
Solution
The diameter of a sphere = 6 cm
Then radius of a sphere`=6/2 cm = 3 cm`
The diameter of a wire = 2 mm
Then radius of wire = 1 mm = 0.1 cm
Now,
Volume of sphere = volume of wire
`4/3 pir^3 = pi r^2 h`
Here,
r = radius
l = length of wire
`4/3 xx 3xx 2 = 0.1 xx 0.1 xx l`
`36 = 0.01 l`
`l = 36/0.01`
To remove the decimal from base we should multiply both numerator and denumerator by 100,
We get,
`l = 3600 = 36m`
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