Q14 of 26 Page 183

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.

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×r3


Volume of big sphere = (4/3)×π×(8)3 cm3


Volume of small sphere = (4/3)×π×(1)3 cm3


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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