Question

3. The diameter of metallic sphere is 6cm. It is melted and drawn into the

wire having diameter of 0.2 cm. Find the length of the wire.​

Answer 1

Answer:-

$\red{\bigstar}$ Length of the wire is $\large\leadsto\boxed{\tt\green{3600 \: cm \:or \: 36 \: m}}$

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• Given:-

• Diameter of metallic sphere = 6 cm

• Diameter of wire = 0.2 cm

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• To Find:-

• Length of the wire

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• Solution:-

Given that,

Diameter of metallic sphere is 6 cm.

Hence,

Radius of the metallic sphere = d/2

➠ 6/2

➠ 3 cm

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Also,

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Diameter of the wire is 0.2 cm

Therefore,

Radius of cylindrical wire = d/2

➠ 0.2/2

➠ 0.1 cm

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Now, the metallic sphere is melted into cylindrical wire.

Hence,

★ Volume of sphere = Volume of Cylinder

$\pink{\bigstar}$ $\large\underline{\boxed{\bf\green{\dfrac{4}{3} \pi r^{3} = \pi r^2 h}}}$

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• Substituting in the Formula:-

➠ $\sf \dfrac{4}{3} \times \pi \times (3)^3 = \pi \times (0.1)^2 \times h$

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➠ $\sf \dfrac{4}{3} \times \pi \times 27 = \pi \times 0.01 \times h$

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➠ $\sf 4 \times \pi \times 9 = \pi \times 0.01 \times h$

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➠ $\sf 36 \: \pi = \pi \times 0.01 \times h$

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➠ $\sf h = \dfrac{36 \: \pi}{0.01 \: \pi}$

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➠ $\sf h = \dfrac{36}{0.01}$

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➠ $\bf h = 3600$

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★ $\large{\bf\purple{h = 3600 \: cm \: or \: 36 \: m}}$

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Therefore, length of the wire is 3600 cm or 36m.

Answer 2

Given,

Diameter of metallic sphere =6cm

Radius of metallic sphere =3cm

Diameter of melted wire = 0.2cm

Radius of melted wire = 0.1cm

Volume of the metal used in wire= Volume of the sphere

$π× {r}^{2} ×h= \frac{4}{3} ×π× {r}^{3}$

$π× {(0.1)}^{2} ×h= \frac{4}{3} ×π× {3}^{3} </p><p>$

$π× { (\frac{1}{10} )}^{2} ×h= \frac{4}{3} ×π×27$

$π× \frac{1}{100 } ×h=36π</p><p></p><p></p><p>$

$h= \frac{36π×100}{\pi} cm=3600cm=36metres</p><p></p><p></p><p>$