Question

How many solid sphere of radius of 1 cm will be formed by melting a solid metallic sphere of radius 8cm?

Answer 1

Hey


Radius of small sphere ( r ) = 1 cm


Volume of small spheres

= 4 / 3 * pie * ( r ) ³


= 4 / 3 * pie * ( 1 ) ³


= 4 / 3 * pie


Now ,


Radius of larger sphere ( R ) = 8 cm


Volume of larger sphere

= 4 / 3 * pie * ( 8 ) ³


= 4 / 3 * pie * 512


Now ,


number of spheres required


= Volume of larger sphere / volume of smaller sphere



= 4 / 3 * pie * 512 / 4/3 * pie


= 512



thanks :)

Answer 2

Volume of big sphere (V1) = 4/3×pie×r×r×r
= 4/3×pie×8×8×8
= 2048/3 × pie

Volume of small sphere (V2) = 4/3×pie×r×r×r
= 4/3×pie×1×1×1
4/3×pie

No. Of sphere = V1÷V2
= 2048/3×pie ÷ 4/3×pie
= 2048÷4 [ 3 cancels with 3 and pie
cancels with pie]
= 512

Hope it helps.
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