Question

pls solve it
i didn't get it​

Answer 1

Solution:

Let radius of large spherical ball = R

$\sf{So,\;volume\;of\;large\;ball=\dfrac{4}{3}\pi r^{3}}$

$\sf{\implies \dfrac{4}{3} \pi r^{3}}$

Now, it is given in question that the radius of smaller ball  = r/2

$\sf{Now,\;volume\;of\;small\;ball=\dfrac{4}{3}\pi r^{3}}$

$\sf{\implies \dfrac{4}{3}\pi \times \Big(\dfrac{r}{2}\Big)^{3}}$

$\sf{\implies \dfrac{4}{3}\pi \times \dfrac{r^{3}}{8}}$

$\sf{\implies \dfrac{\pi r^{3}}{6}}$

∴ Now, number of balls = Volume of original spherical ball / Volume of Smaller balls.

$\sf{\implies Number\;of\;balls=\dfrac{\dfrac{4}{3}\pi r^{3}}{\dfrac{\pi r^{3}}{6}}}$

$\sf{\implies Number\;of\;balls=\dfrac{4}{3}\times 6}$

$\large{\boxed{\boxed{\sf{\red{\implies Number\;of\;balls=8}}}}}$

Answer 2

Question:-

A spherical ball of lead is melted and made into identical smaller balls with radius half the radius of the original one. How many such balls can be made?

Explanation:-

Let us consider that

Radius of the sphere before it was melted=r

$\bullet \sf volume,V_1 =\dfrac{4}{3}\pi r^3$

After it was melted,

small balls were made of radius half the original one

So,radius=r/2

$\bullet \sf volume,V_2=\dfrac{4}{3}\pi (\dfrac{r}{2})^3$

$\bullet \sf V_2=\dfrac{4}{3}\pi× \dfrac{r^3}{8}$

Now

$\boxed{\bf number \:of \:spheres =\dfrac{V_1}{V_2}}$

$\boxed{\bf n=\dfrac{Volume \: of \: big \: sphere}{volume \:of \:small \:sphere}}$

$\sf no.of \: balls=\dfrac{\dfrac{4}{3}\pi r^3}{\dfrac{4}{3}\pi ×\dfrac{r^3}{8}}$

$\sf =>\dfrac{1}{(\dfrac{1}{8})}=8$

$\boxed{\sf no.of \:balls=8}$