A solid sphere of radius 3 cm is melted and then cast into smaller spherical balls,

Question:

A solid sphere of radius 3 cm is melted and then cast into smaller spherical balls, each of diameter 0.6 cm. Find the number of small balls thus obtained.

Solution:

Radius of the solid sphere = 3 cm

Volume of the solid sphere $=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times 3^{3} \mathrm{~cm}^{3}$

Diameter of the spherical ball = 0.6 cm
Radius of the spherical ball = 0.3 cm

Volume of the spherical ball $=\frac{4}{3} \times \frac{22}{7} \times(0.3)^{3} \mathrm{~cm}^{3}$

Now, number of small spherical balls $=\frac{\text { volume of the sphere }}{\text { volume of the spherical ball }}$

$=\frac{\frac{4}{3} \pi \times 27}{\frac{4}{3} \pi \times\left(0.3^{3}\right)}$

$=1000$

∴ The number of small balls thus obtained is 1000

 

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