Question

How many balls each of radius 2 centimetre can be made from a solid sphere of lead of radius 8 centimetre

Answer 1

Radius of solid sphere = 8cm
Volume = 4/3πr³ = 4/3 π x 8 x 8 x 8 cm³ = 4/3 π x 512

Radius of ball = 2cm
Let the number of balls be a
Then, volume of 'a' balls =
4/3πr³ x a = 4/3 π x 2 x 2 x 2x a  = 4/3 π x 8 x a cm³

Volume of sphere = Volume of 'a' balls
4/3 π x 8 x a = 4/3 π x 512
8a = 512
a = 64

∴ 64 balls can be made.

Hope This Helps!

Answer 2

Given:

Balls have a radius of 2 centimetres and a solid sphere of lead has a radius of 8 centimetres.

To find:

The number of balls that can be made from a solid sphere of lead.

Solution:

As we know that balls are in the form of a sphere and the volume of a sphere having radius 'r' is given by:

$= \frac{4}{3} \pi \: {r}^{3}$

Now,

as given, we have,

The radius of one ball = 2 cm

So,

The volume of one ball

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

$= \frac{4}{3} \pi \times 8 {cm}^{3} \: \: (i)$

Also,

the radius of a solid sphere of lead = 8 cm

So, the volume of a solid sphere of lead

$= \frac{4}{3} \pi {(8)}^{3}$

$= \frac{4}{3} \pi \times (8 \times 8 \times 8) \: {cm}^{3} \: \: (ii)$

So,

the number of balls that can be made from a solid sphere

$= \frac{area \: of \:a \: solid \: sphere}{area \: of \: one \: ball}$

$= \frac{ \frac{4}{3} \pi \times (8 \times 8 \times 8) \: {cm}^{3} }{ \frac{4}{3} \pi \times 8 {cm}^{3} }$

...from (i) and (ii)

$= 64$

Hence, the number of balls that can be made from a solid sphere of lead is 64.