Q. 21

# A copper sphere of diameter 18 cm is drawn into wire of diameter 4 mm. Find the length of the wire.

Answer :

__The basic concept required to solve any such question is that the volume of the two figures will be same, so here we will equate the volume of sphere to that of wire which is in shape of a cylinder and subsequently will find out the height of the cylinder.__

Given diameter of copper sphere = D = 18 cm

∴ Radius of the sphere = R = d/2=18/2 = 9 cm

As we know the wire is cylindrical in shape so,

Let the height of the cylindrical wire be ‘h’ cm

Given diameter of cylindrical wire = d = 4 mm

⇒ Radius of the cylindrical wire = r = d/2= 4/2= 2 mm= 0.2 cm (∵ 1 mm = 0.1 cm)

Volume of a sphere=(where R=radius of sphere)→eqn1

(putting value of R in eqn 1)

⇒ Volume of sphere = 4π × 243= 972π cm^{3}→eqn2

Volume of cylinder = πr^{2}h

Where r = radius of base of cylinder and h = height of cylinder

⇒ Volume of cylindrical wire = π × (0.2)^{2} × h (putting value of r)

= 0.04π × h cm^{3}→eqn3

Now on equating equation 2 and equation 3, we get,

Volume of sphere = Volume of cylindrical wire

⇒ 972π = 0.04πh

⇒ π(927) = π(0.04h) (taking π common on both sides)

⇒ 927 = 0.04h

∴ h = 24300 cm

__The height of cylindrical wire is 24300 cm or 243 m.__

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