Question

3. A solid sphere of radius 3 cm is melted and then recast into small spherical balls, each of

diameter 0.6 cm. Find the number of small balls so obtained.​

Answer 1

1000

Explanation:

`Volume \: of \: solid \: sphere \\ = (4)/(3) \pi {r}^(3) \\ \\ = (4)/(3) \pi ({3})^(3) \\ \\ = (4)/(3) \pi * 27 \: {cm}^(3) \\ \\ diameter \: of \: one \: small \: ball \\ = 0.6 \: cm \\ \therefore \: radius \: (r) = 0.3 \: cm \\ \\ Volume \: of \: one \:small \: ball \\ = (4)/(3) \pi {r}^(3) \\ \\ = (4)/(3) \pi ({0.3})^(3) \\ \\ = (4)/(3) \pi * 0.027 \: {cm}^(3) \\ \\ number \: of \: balls \\ \\ = (Volume \: of \: solid \: sphere)/(Volume \: of \: one \:small \: ball ) \\ \\ = \frac{(4)/(3) \pi * 27 \: {cm}^(3) }{(4)/(3) \pi * 0.027 \: {cm}^(3) } \\ \\ = (27)/(0.027) \\ \\ = (27000)/(27) \\ \\ = 1000`