A-solid-sphere-of-radius-4-cm-is-melted-and-recast-into-n-solid-hemispheres-of-radius-2-cm-each-Find-n-

Question Number 16418 by Mr easymsn last updated on 21/Jun/17

A solid sphere of radius 4 cm is melted

and recast into^{'} n^{'} solid hemispheres of

radius 2 cm each . Find n .

Answered by Tinkutara last updated on 22/Jun/17

Volume of solid sphere = Volume of n

hemispheres

\frac{4}{3} π {(4)}^{3} = \frac{n}{2} \times \frac{4}{3} π {(2)}^{3}

n = 2 \times {(\frac{4}{2})}^{3} = 16

Commented by mrW1 last updated on 22/Jun/17

I think the question is

one sphere with radius 4 = n hemisphere with radius 2

\equiv one sphere with radius 4 = \frac{n}{2} sphere with radius 2

\Rightarrow \frac{4}{3} π {(4)}^{3} = \frac{n}{2} \times \frac{4}{3} π {(2)}^{3}

\Rightarrow n = 2 {(\frac{4}{2})}^{3} = 16

Commented by Tinkutara last updated on 22/Jun/17

Thanks Sir! It is now corrected .