Question

The radius of a metallic sphere is 8 cm it is melted and recast into a small marbles having diameter of 1 cm how many marbles are formed

Answer 1

Ans.

The radius of the metallic marble (r) = 8 cm
Then, its volume (v)
$= \frac{4}{3} \pi {r}^{3} \: \: {cm}^{3} \\ = \frac{4}{3} \pi \times {8}^{3} \: \: {cm}^{3}$

The radius of a small marble (s) = 0.5 cm
Then, its volume (k)
$= \frac{4}{3} \pi {s}^{3} \: \: {cm}^{3} \\ = \frac{4}{3} \pi \times {0.5}^{3} \: \: {cm}^{3}$

Let, n numbers of small marbles are made.

Then,
v = n.k
$or \: \: {8}^{3} = n \times {0.5}^{3} \\ or \: \: n = \frac{ {8}^{3} }{ {0.5}^{3} } \\ or \: \: n = 4096$
So, 4096 small marbles will be formed.

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