Question

A sphere made of gold measuring 6 cm in diameter, was molten to form the shape of a wire. If the wire had a radius of 0.25 cm, what was its length (in cm)?​

Answer 1

Answer:

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Explanation:

$to \: find = \\ length \: of \: wire \: (h) \\ \\ given = \\ for \: a \: certain \: sphere \: \\ diameter \: (d) = 6.cm \\ thus \: then \\ radius \: (r) = 3.cm \\ \\ for \: cylindrical \: wire \\ radius \: (r1) = 0.25 \: cm$

$so \: as \: sphere \: is \: molten \: and\:recasted \: into \: wire \\ their \: volumes \: would \: be \: equal \\ \\ so \: thus \\ volume \: of \: sphere = \frac{4}{3} \: \pi.r {}^{3} \\ \\ volume \: of \: wire = volume \: of \: cylinder = \pi.r {}^{2} h \\ \\ hence \: accordingly \\ \\ \frac{4}{3} \: \pi.r {}^{3} = \pi.r 1{}^{2} h \\ \\ \frac{4}{3} \times (3) {}^{3} = (0.25) {}^{2} \times h \\ \\ 4 \times 9 = 0.0625h \\ \: \: 36 = 0.0625h \\ \\ h = \frac{36}{0.0625} \\ \\ h = 576 \: cm \\ = 5.76 \: m$

$hence \: length \: of \: wire \: is \: 576 \: cm \: ie \: 5.76 \: m$