Question

18. The diameter of a copper sphere is 18 cm. It is melted and drawn into a
long wire of uniform cross section. If the length of the wire is 108 m,
find its diameter​

Answer 1

Diameter of a copper sphere is 18 cm.

$\implies$ d = 18 cm

$\implies$ r = 18/2 = 9 cm

The copper wire is melted and drawn into a long wire of length 108 m.

$\implies$ l = 108 m

$\implies$ l = 10800 cm

[As, 1 m = 100 cm]

• Let the radius of cylindrical wire be "r" and radius of copper sphere be "R".

Now,

Volume of cylindrical wire = Volume of copper sphere

$\Rightarrow$ πr²h = 4/3πR³

Put the known values in above formula

→ 22/7 × r² × 10800 = 4/3 × 22/7 × (9)³

→ r² × 10800 = 4/3 × 729

→ r² × 10800 = 4 × 243

→ r² × 10800 = 972

→ r² = 972/10800

→ r² = 0.09

→ r = 0.3 cm

So,

$\implies$ Diameter = 2 × radius

$\implies$ Diamter = 2 × 0.3 = 0.6 cm

∴ 0.6 cm is the diameter of the wire

Answer 2

Answer:

Step-by-step explanation: