Question

how many balls of each radius 1 cm can be made from a solid sphere of lead of radius 8 cm

Answer 1

512 balls can be made.

Solution:

We know that,

Volume of solid sphere with r radius $=\frac{4}{3}\left(\pi r^{3}\right) \ldots \ldots . . .(1)$

So,

Volume of solid sphere with radius 8 cm $=\frac{4}{3}\left\{\pi\left(8^{3}\right)\right\} \dots \ldots \ldots \ldots(2)$

Volume of ball of radius 1 cm$=\frac{4}{3}\left\{\pi(1)^{3}\right\} \ldots \ldots \ldots \ldots(3)$

Let, n ball of each radius 1 cm could be made from the ‘solid sphere’.

Therefore,

From equation (2) and (3) -

$\frac{4}{3}\left\{\pi\left(8^{3}\right)\right\}=n \times \frac{4}{3}\left\{\pi(1)^{3}\right\}$

$8^{3}=n$

n = 512

Hence 512 balls of radius 1 cm can be made from a “solid sphere of radius 8 cm”.

Answer 2

Answer:

Number of small balls required to

Number of small balls required tomake a solid lead sphere (n)=512

Explanation:

Given radius of the each small

ball (r) = 1cm

Radius of lead solid sphere made by small balls (R)=8cm

Let number of small balls required to made solid lead sphere = n

______________________

We know that,

$\boxed {Volume \:of \: the\: sphere \:(V)\\\\= \frac{4}{3}\times \pi \times (radius)^{3}}$

________________________

Now ,

$n = \frac{Volume\: of\: solid \:sphere}{Volume\: of\: each \:small \:ball}$

$\implies n = \frac{\frac{4}{3}\times \pi R^{3}}{\frac{4}{3}\times \pi r^{3}}$

$\implies n = \frac{R^{3}}{r^{3}}$

$\implies n = \frac{8^{3}}{1^{3}}$

$\implies n = 8\times 8 \times 8$

$\implies n = 512$

Therefore,

Number of small balls required to

make a solid lead sphere (n)=512

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