Question

if a solid sphere of diameter 28cm is melted and recost into smaller spheres of radii 2cm. Find the no. of sphere produced. ​

Answer 1

Answer:

343 spheres

Step-by-step explanation:

solid sphere                                        smaller sphere

D = 28cm                                                    r = 2cm

Volume of "n" smaller sphere = volume of solid sphere

        n x 4/3  π r ³                      =  4/3 π R³

      n x 4/3 π x 2x2x2                = 4/3 π x 14 x14 x14

                   ∴   n  = ( 14 x14 14)   / ( 2x2x2)

                            =  343 spheres

Answer 2

$\large{\blue{\implies{Given}}}$

A solid sphere of radius 28cm melted and recast into smaller spheres of radius 2cm

$\large{\implies{\blue{To\:find}}}$

✨ Number of spheres

$\huge{\mathcal{\blue{\underline{Answer}}}}$

Radius of Larger sphere =D/2= 28cm/2 = 14cm

The volume of the larger sphere :

$= \frac{4}{3} \pi \: r {}^{3} \\ = \frac{4}{3} \pi \: (14cm) {}^{3}$

The Volume of the smaller spheres of radii 2cm

$= \frac{4}{3} \pi \: r {}^{3} \\ = \frac{4}{3} \pi \: (2cm) {}^{3}$

Number of sphere = volume of larger sphere/volume of smaller sphere

$= \frac{ \frac{4}{3}\pi \: (14cm) {}^{3} }{ \frac{4}{3} \pi \: (2cm) {}^{3} } \\ = \frac{2744cm {}^{3} }{8cm {}^{3} }$

$\huge{\mathcal{\orange{\implies{\underline{343Spheres}}}}}$