Question

how many balls of radius 1mm can be prepared by melting a sphere of radius 1cm.​

Answer 1

in this case the tot volume should remain. same

4/3πr³ n = 4/3πR³

solving we her n ,= 10³

hence 1000 balls can be made

r = radius of small ball R ,= of phere

Answer 2

❏ Question:-

@ How many balls of radius 1mm can be prepared by melting a sphere of radius 1cm.

❏ Solution:-

$\bf{Given}\begin{cases}\text{Radius Of Large Sphere R=1 cm} \\ \text{Radius of Small Sphere r=1 mm =0.1 cm}\end{cases}$

Let, the number of balls is = N pcs.

Now, The volume of the large sphere is

$\sf\implies V_{large}= \frac{4}{3}\times\pi\times R^3$

$\sf\implies V_{large}= \frac{4}{3}\times\pi\times 1^3\:cm^3$

$\sf\implies \boxed{\red{V_{large}= (\frac{4\pi}{3})\:cm^3}}$

Now, for the Each of small sphere,

The volume of each small sphere is ,

$\sf\implies V_{small}= \frac{4}{3}\times\pi\times r^3$

$\sf\implies V_{small}= \frac{4}{3}\times\pi\times (0.1)^3\:cm^3$

$\sf\implies \boxed{\red{V_{small}= (\frac{4\pi}{3000})\:cm^3}}$

Therefore, Number of small spherical balls is,

$\sf\implies N= \frac{\cancel{\frac{4}{3}\pi} R^3}{\cancel{\frac{4}{3}\pi} r^3}$

$\sf\implies N= \frac{ R^3}{r^3}$

$\sf\implies N=(\frac{ R}{r})^3$

$\sf\implies N=(\frac{ 1}{0.1})^3\:pcs$

$\sf\implies N=(10)^3\:pcs$

$\sf\implies\boxed{\large{ \red{N=1000\:pcs}}}$

∴ Number of small balls is = 1000 pcs.

$\setlength{\unitlength}{0.8cm}\begin{picture}(10,5)\thicklines\qbezier(1,1)(1,1)(9,1)\end{picture}$