Q. 85.0( 2 Votes )

# The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.

Answer :

Given: diameter of sphere = 42 cm

∴ radius of sphere = 42/2 = r_{s} = 21 cm

Diameter of cylindrical wire = 2.8 cm

∴ Radius of cylindrical wire = r_{c} = 1.4 = (7/5)cm

Let l be the length of wire

Formula: volume of sphere = (4/3)πr_{s}^{3}

Volume of wire = πr_{c}^{2}l

Sphere is melted and wire is made from it

∴ volume of sphere = volume of wire

(4/3)πr_{s}^{3} = πr_{c}^{2}l

4 × 21^{3} = 3 × (7/5)^{2} × l

4 × 21 × 9 × 25 = 3 × l

2100 × 3 = l

l = 6300 cm

Therefore length of wire formed = 6300 cm = 63 meters

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PREVIOUSA solid metallic sphere of diameter 21 cm is melted and recast into small cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.NEXTA drinking glass is in the shape of frustum of a cone of height 21 cm with 6 cm and 4 cm as the diameters of its two circular ends. Find the capacity of the glass.

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