Question

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

Answer 1

$\large\underline\blue{\bold{Given \:  Question :-  }}$

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

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$\huge{AηsωeR} ✍$

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$\large\underline\blue{\bold{Given :-  }}$

The radius of the sphere is 7 cm.

It is melted and drawn into a wire of radius 0.3 cm.

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$\large\underline\blue{\bold{To \: Find :-  }}$

The length of the wire.

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$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

${{ \boxed{\large{\bold\red{Volume_{(Cylinder)}\: = \:\pi r^2 h }}}}}$

${{ \boxed{\large{\bold\red{Volume_{(Sphere)}\: = \:\dfrac{4}{3} \pi r^3}}}}}$

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$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\bf let= \begin{cases} &\sf{radius \: of \: cylinder \: = r} \\ &\sf{height \: of \: cylinder \: = h} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf let= \begin{cases} &\sf{radius \: of \: sphere = R} \end{cases}\end{gathered}\end{gathered}$

$\bf \: \red \: According \: to \: statement -$

❥︎Radius of sphere, R = 7 cm

❥︎Radius of wire, r = 0.3 cm

❥︎Since, sphere is melted and recast in to wire, therefore

$\bf \:  ⟼ \blue \: V_{(cylinder)} = V_{(sphere)}$

$\bf\implies \:\pi \: {r}^{2} h = \dfrac{4}{3} \pi \: {R}^{3}$

$\bf\implies \: {r}^{2} h = \dfrac{4}{3} {R}^{3}$

$\bf \:  ⟼ 0.3 \times 0.3 \times h = \dfrac{4}{3} \times 7 \times 7 \times 7$

$\bf\implies \:h = 5081.48 \: cm = 50.48 \: m$

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Answer 2

Answer:

5081.48

Step-by-step explanation:

The length of the wire is 5081.48 cm.

Step-by-step explanation:

Since we have given that

Radius of sphere = 7 cm

Radius of wire =0.3 cm

We need to find the length of the wire,

So, Volume of sphere = volume of wire

=4/3πr³=πr²h

=4/3π*7*7*7=π*0.3*0.3*h

=4*343/3*0.09=h

h=5081.48