Question

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

Answer 1

SOLUTION:-

Given:

Radius of each ball 1cm made from solid sphere lead radius 8cm.

To find:

The balls required a solid sphere.

Explanation:

As we know that, volume of sphere;

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

We have,

•Radius of large sphere, r1= 8cm.

•Radius of small sphere, r2= 1cm.

So,

Number of small balls that can be made from the big solid sphere:

$\frac{Volume \: of \: big \: sphere}{Volume \: of \: one \: small \: sphere} \\ \\ = > \frac{ \frac{4}{3} \pi {r1}^{3} }{ \frac{4}{3} \pi {r2}^{3} } \\ \\ = > \frac{r1 {}^{3} }{r2 {}^{3} } \\ \\ = > \frac{{8}^{3} }{ {1}^{3} } \\ \\ = > 8 \times 8 \times 8 = 512 \: spheres$

Thus,

The balls required to make a solid sphere is 512 balls.