Q. 144.4( 19 Votes )

# Let us write by calculating how many marbles with lengths of 1 cm. radius may be formed by melting a solid sphere of iron having 8 cm length of radius.

Answer :

__Given:__

Radius of small marbles = 1cm

Radius of big sphere = 8cm

__Formula used:__

Volume of big sphere = Volume of small spheres × No. of marbles

We know that Volume of sphere = (4/3)×π×r^{3}

Volume of big sphere = (4/3)×π×(8)^{3} cm^{3}

Volume of small sphere = (4/3)×π×(1)^{3} cm^{3}

Putting the values,

⇒ (4/3)×π×(8)^{3} = (4/3)×π×(1)^{3} × No. of marbles

⇒ No. of small marbles = (8)^{3}/(1)^{3} = 512

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