Question

The radius of the sphere is 7 cm. It is melted and drawn into a wire of radius 0.3 find the length of the wire

Answer 1

$Radius \: of \:the \: Sphere (R) = 7\:cm$

/* If Sphere is melted and drawn into a wire */

$Radius \: of \:the \: wire (r) = 0.3\:cm$

$Let \: length \: of \: the \: wire = h \: m$

$\pink { Volume \: of \: the \: wire (cylinder ) }\\= \blue {Volume \: of \:the \: Sphere }$

$\implies \pi r^{2} h = \frac{4}{3} \pi R^{3}$

$\implies r^{2} h = \frac{4}{3} R^{3}$

$\implies h = \frac{4 \times R^{3}}{3 \times r^{2}}\\= \frac{ 4 \times 7^{3}}{3 \times (0.3)^{2}}\\= \frac{4 \times 7 \times 7 \times 7 }{3 \times 0.3 \times 0.3}\\= \frac{1372}{0.27} \\= 5081.48\: cm$

Therefore.,

$\red {Length \: of \: the \: wire} \green {= 5081.48\: cm}$

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Answer 2

$\huge\bold\green{Question}$

The radius of the sphere is 7 cm. It is melted and drawn into a wire of radius 0.3 find the length of the wire ?

$\huge\bold\green{Answer}$

According to the question we have given :-

•°• Radius of Sphere (R) = 7cm

Now as said in question the sphere is melted and drawn into a wire [cylindrical shape]

•°• Radius of wire (r) = 0.3 cm

$\tt{Let \: length \: of \: the \: wire = h \: }$

As we know that :-

$\begin{lgathered}\tt{ Volume_{wire}} = \tt{Volume_{sphere}}\end{lgathered}$

Now by using their formulas we get :-

$\longrightarrow\tt{\pi r^{2} h = \frac{4}{3} \pi R^{3}}$

= $\tt\implies{ r^{2} h = \frac{4}{3} R^{3}}$

$\begin{lgathered}\tt\implies h = \frac{4 \times R^{3}}{3 \times r^{2}}\\ \\ \tt = \frac{ 4 \times 7^{3}}{3 \times (0.3)^{2}}\\ \\ \tt = \frac{4 \times 7 \times 7 \times 7 }{3 \times 0.3 \times 0.3}\\ \\ \tt = \frac{1372}{0.27} \\ \\ \tt = 5081.48\: cm\end{lgathered}$

Hence the required length of wire is 5081.48 cm