Question

a solid sphere of radius 1 cm is melted to stretch into a wire of length 100 cm , find the radius of the wire.

Answer 1

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Answer 2

AnswEr:

We have,

Radius of the solid sphere = 1 cm

$\therefore$ Volume of the solid sphere

$= \sf \dfrac{4}{3} \times \dfrac{22}{7} \times 1 \times 1 \times 1 \: {cm}^{3} \\ \\ = \sf \dfrac{88}{21} \: {cm}^{3}$

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◕ Clearly, the wire is a cylinder of length 100 cm.

Let the radius of the wire be r cm. Then,

Volume of the wire = $\sf\dfrac{22}{7}\times\:r^2\times\:100\:cm^3$

= $\sf\dfrac{2200}{7}r^2\:cm^3$

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But, Volume of the wire = Volume of the solid sphere

$\implies \sf \dfrac{220}{7} {r}^{2} = \dfrac{88}{21} \\ \\ \implies \sf {r}^{2} = \frac{88}{21} \times \frac{7}{2200} \\ \\ = \sf \: \frac{1}{75} \\ \\ \implies \sf \: r = \sqrt{ \frac{1}{75} } cm \\ \\ = \sf\frac{1}{5 \sqrt{3} } \: cm \\ \\ = \sf 0.11 \: cm$

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