Question

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The diameter of a copper sphere is 6 cm. It is beaten and drawn into a wire of diameter 0.2 cm. Find the length of the wire​

Answer 1

Answer:

length of the wire =3600cm

Step-by-step explanation:

The wire is in the shape of a cylinder.

Since the sphere is melted and a cylindrical wire is formed, their volumes are equal.

Volume of a sphere of radius 'r' -

$n \frac{4}{3} \pi {r}^{3}$

As the diameter of the sphere is 6 cm, its radius r =3 cm

Volume of a cylinder of radius "R" and height "h" =πR²h

Radius of the wire =

$\frac{0.2}{2} = 0.1cm$

Hence, Volume of sphere = Volume of the wire

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

$\frac{4}{3} \pi \times {3}^{3} = \pi \times {0.1}^{2} \times h$

h=3600cm

Hence, length of the wire =3600cm

Answer 2

✯Question✯

• The diameter of a copper sphere is 6 cm. It is beaten and drawn into a wire of diameter 0.2 cm. Find the length of the wire​ ?

✮Given✮

• Diameter = 6cm   (copper sphere)
• Diameter of beaten wire = 0.2cm

✬To find✬

• Length of the wire

✭Solution✭

• Sphere is melted and a cylindrical wire is formed, their volumes are equal:

• Volume of copper wire = Volume of copper sphere
• πr²h = ⁴⁄₃πr³
• 0.1²h = ⁴⁄₃×3³
• h = 4 × 9 ÷ 0.01
• h = 3600

✱Length of the wire is 3600cm✱

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➺The diameter of a copper sphere is 6 cm. it is melted and drawn into a long wire of uniform circular cross section. if the length of the wire is 36cm, then find the radius ?