Question

A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of diameter 0.6cm .Find the no of balls

Answer 1

For Sphere

Radius = 3 cm

So,

$\huge \boxed{Volume = \frac{4}{3} \times \pi \times r^{3}}$

$\mathsf{Volume = \dfrac{4}{3} \times \dfrac{22}{7}\times 3^{3}}$

$\mathsf{Volume = \frac{4}{3} </p><p>\times \frac{22}{7}\times 27 }$

$\huge \boxed{Volume = 113.14 cm^{3}}$

For small sphere

Diameter = 0.6

$\frac{0.6}{2}$

Radius = 0.3cm

$\huge \boxed{Volume = \dfrac{4}{3} \times \pi \times r^{3}}$

$\mathsf{Volume = \dfrac{4}{3} \times \dfrac{22}{7}\times 0.3^{3}}$

$\mathsf{Volume = \dfrac{4}{3} </p><p>\times \dfrac{22}{7}\times 0.027 }$

$\huge \boxed{Volume = 0.11314cm^{3}}$

Given, that the sphere is melted and made to x number of spheres ,

So,

$\huge \boxed{No \: of \: spheres = \dfrac{Volume \: of \: original \: sphere}{Volume \: of \: 1 \: small \: sphere}}$

$\mathsf{No \: of \:sphere= \dfrac{113.14}{0.13314}}$

$\boxed{ \mathsf{No \: of \:sphere= 1000}}$

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Suppose radius big sphere

(R) = 3 cm

Suppose radius of smaller balls

$\bf\huge{\implies r =\dfrac{0.6}{2}}$        

= 0.3 cm

Suppose number of small balls be p

$\bf\huge{\implies p\times\dfrac{4}{3}\pie r^3 = \dfrac{4}{3}\pie r^3}$        

After cancellation we get

$\bf\huge{\implies p = \dfrac{R^3}{r^3}}$        

$\bf\huge{\implies p = (\dfrac{R}{r})^3}$  

$\bf\huge{\implies p = (\dfrac{3}{0.3})^3}$  

= (10)^3

= 1000

Hence

$\bf\huge\bf\huge{\boxed{\bigstar{{No \:of\: balls = 1000}}}}$