a sphere of diameter 6.0cm is moulded into a thin uniform wire of diameter 0.2mm calculate the length of the wire in metres [take pie =22/7] . pliz kindly help
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Volume of sphere = 4/3 x pi x r^3
=4/3 x 22/7 x 3 x 3 x 3
=4 x 22/7 x 3 x 3 (3 gets cancelled out)
= (88 x 9)/7
=113.14cm^2 approx.
Volume of wire = pi x r^2 x h (h is taken as length of wire) = Volume of sphere
= 22/7 x 0.01 x 0.01 x h = 113.14cm^2
= 0.0022/7 x h = 792/7 (taken as fractional form for ease of calculation)
= pi x 0.001 x h = 792/7
= 0.001h = 792/7 x 7/22 (reciprocal of pi)
= h = 36/0.001
= h = 3600mm / 3.6m
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when we mold a sphere into a wire its volume remains same
by using this concept volume of sphere=volume of cylinder(let us consider wire as cilinder)
ie: 4/3πr³=πb²h r=radius of sphere=3cm b=radius of the wire=0.01cm and h=height/length of the cylinder.
4/3 π 3³=π 0.01² h
h=[4/3×3³]/0.01²=360000cm
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