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

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Given :

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

wire having diameter of 0.2 cm.

To Find :

The length of the wire

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Formula used here :

$\bold{\boxed{\pink{Volume \:Of \:Sphere = \frac{4}{3} \pi {r}^{3}}}}$

$\bold{\boxed{Volume\: of\: Cylinder =\pi {r}^{2} h}}$

Diameter of metallic sphere =6cm

We know that diameter is twice of radius

e.g =>D=2r

$6 cm= 2r$

$radius = 3cm$

Note :Wire is in the shape of cylinder

Diameter of wire =0.2cm

Radius of wire =0.1cm

Now , metallic sphere is melted into the shape of cylinder so,there will be no effect on its area.

Area of metallic sphere will be equal to the cylinder.

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

Cancelling pie on both sides :

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

$= > \frac{4}{3} {(3)}^{3} = {(0.1)}^{2} h$

$= > \frac{4}{3} \times 27 = 0.01h$

$= > 36 = 0.01h$

$= > h = \frac{36}{0.01} = \frac{3600}{1} = 3600cm$

∴The length of the wire is $\bold{\green{3600\:cm }}$ or$\bold{\green{ 36\: metre}}$