Question

The diameter of a metal sphere is 6
cm. Itis melted and drawn into a wire
of diameter 2 mm. The length of the
wire is​

Answer 1

Given:

The diameter of a metal sphere is 6 cm

So,

The radius of the sphere = diameter/2

Radius of the sphere(R) = 6/2 = 3cm = 30 mm

We

1 cm = 10 mm

∵ 3 cm = 30 mm

Now,

To find:

The length of the wire (h) when the same sphere is melted and drawn into a wire of diameter 2mm.

The radius of the wire (r) = 2/2 = 1 mm

Now,

The volume of the wire and the sphere is the same

The wire is a cylindrical shape,

⇒ πr²h = 4/3 πR³

⇒ r²h = 4/3 R³

[∵ In both side π will be cancelled out]

⇒ 1² * h = 4/3 * (30)³

⇒ h = 4 * 9000

⇒ h = 36000 mm

Hence,

The length of the wire(h) is 36000 mm

36000 mm = 3600 cm = 36 m

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More Information

• Curved Surface Area of a cylinder = 2πrh unit sq.
• Total Surface Area of a cylinder = 2πh(r+h) unit sq.

Answer 2

Answer:

When one Solid shape is melted and converted into other Solid shape then Volume remains unchanged.

• According to the Question :

⇒ Volume of Sphere = Volume of Wire

⇒ 4/3 πR³ = πr²h

⇒ 4/3 R³ = r²h

⇒ 4/3 (D/2)³ = (d/2)²h

⇒ 4/3 (6 cm/2)³ = (2 mm/2)²h

⇒ 4/3 (3 cm)³ = (1 mm)²h

• Changing into cm (1cm = 10mm)

⇒ 4/3 × 3 × 3 × 3 cm³ = 1 × 1 × 1/100 cm² × h

⇒ 4 × 3 × 3 cm³ = 1/100 cm² × h

⇒ 36 cm × 100 = h

⇒ 3600 cm = h

• Changing into m (1m = 100cm)

⇒ h = 36 m

∴ Length if wire drawn is 36 metres.