Question

A sphere of radius r is melted and 8 spherical balls of same radii are formed. Find radius of each spherical ball​

Answer 1

Answer:

r/8 is the radius of each spherical ball

Answer 2

Radius of each spherical ball​ is $\dfrac{r}{2\sqrt{2}}$ unit.

Step-by-step explanation:

Since, when some spheres of same size is formed from a sphere,

Then,

$\text{Number of such sphere}=\frac{\text{Volume of big sphere}}{\text{Volume of each small sphere}}$

Now, volume of a sphere,

$V=\frac{4}{3}\pi R^3$

Where, R = radius of the sphere,

We have,

radius of big sphere = r unit,

So, its volume = $\frac{4}{3}\pi r^3$

Consider x be the radius of the smaller sphere,

Volume of each small sphere = $\frac{4}{3}\pi x^3$

Also, Number of such sphere =8,

By substituting the values in the above formula,

$8=\frac{\frac{4}{3}\pi r^2}{\frac{4}{3}\pi x^2}$

$8 =\frac{r^2}{x^2}$

$x^2 =\frac{r^2}{8}$

$\implies x =\sqrt{\frac{r^2}{8}}=\frac{r}{2\sqrt{2}}$

Hence, radius of each spherical ball​ is $\dfrac{r}{2\sqrt{2}}$ unit.

#Learn more:

100 small cubes each of volume is 8 m cube, are put together to form a cuboid. find the volume of the cuboid thus formed.

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