Question

20. How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm​

Answer 1

Answer:-

★ Given:-

A solid sphere of radius, R = 8 cm

With this sphere, we have to make spherical balls of radius r = 1 cm

Let’s assume that the number of balls made as n

Then, we know that

Volume of the sphere = 4/3 πr3

The volume of the solid sphere = sum of the volumes of n spherical balls.

n x 4/3 πr3 = 4/3 πR3

n x 4/3 π(1)3 = 4/3 π(8)3

n = 83 = 512

Therefore, 512 balls can be made of radius 1 cm each with a solid sphere of radius 8 cm.

Answer 2

$\Large{\underline{\textsf{\textbf{\red{Required Solution:-}}}}}$

$\frak{\pink{Given}} \begin{cases} \sf {\orange{A\; solid\; sphere \;of \;radius, R = 8 cm}}\\ \sf{\orange{With ~this~ sphere, we ~have ~to ~make~ spherical~ balls ~of ~radius ~r = 1 cm}}\end{cases}$

Let’s αssume thαt the number of bαlls mαde αs 'n'.

Then, we know thαt,

$:\leadsto \small{\sf{ Volume\; of\; the\; sphere = \dfrac{4}{3} \pi\; r^3}}$

$\small{\sf{The~ volume ~of ~the~ solid ~sphere = sum ~of~ the~ volumes ~of~ n ~spherical~ balls.}}$

$: \leadsto \small{\sf{n \times \dfrac{4}{3} \pi \;r^3 = \dfrac{4}{3} \pi \; R^3}}$

$:\leadsto \small{\sf{n \times \dfrac{4}{3} \pi \;(1)3 = \dfrac{4}{3} \pi \; (8)3}}$

$:\leadsto \small{\sf{n = 83 = 512}}$

Therefore, 512 bαlls cαn be mαde of rαdius 1 cm eαch with α solid sphere of rαdius 8 cm.

_______________________

Hope it elp! :p