Question

a big solid metal sphere of diameter 48 cm is melted and cast into a small solid of radius 3 cm then the number of small solid spheres formed is -------

Answer 1

Answer:

ans is 8// as d = 48/2 = 24

then 3 × 8 spheres gives the radius 24 cm//

Answer 2

A big solid metal sphere of diameter 48 cm is melted and cast into a small solid of radius 3 cm then the number of small solid spheres formed is 512.

Explanation:

The diameter of the big spherical sphere is 48cm.

Radius of the big spherical sphere r  $=\frac{48}{2} = 24\ cm$.

The volume of the big solid sphere

$= \frac{4}{3} \pi\ r^{3}$

$= \frac{4}{3} \pi\ 24^{3}$  

$=18432\ \pi cm^{3}$

Let the total number of small solid spheres be p.

The radius of small solid R= 3 cm.

The volume of a small spherical sphere

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

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

$=36 \ \pi cm^{3}$

∴ The volume of p small spherical spheres.

$=36 \ \pi \ p \ cm^{3}$

Clearly,

The volume of the big solid sphere = Volume of p spherical spheres.

                                    $18432\ \pi =36 \ \pi \ p$

                                              $p=\frac{18432}{36}$

                                              $p=512$

Hence, 512 small solid spheres are formed by melting the big solid sphere.