Question

2. A solid lead sphere of radius 8 cm is made into a number of spherical pellets each of radius 1 cm.
How many such balls can be made
(1 Point)​

Answer 1

Answer:

512 spherical pellets each of radius 1 cm can be made from a  solid lead sphere of radius 8 cm.

 SOLUTION  

Given

Radius of the solid lead sphere = 8cm.

Radius of spherical pellets made from the solid lead sphere = 1 cm.

$\tt \red\bigstar \boxed{Volume \:of\: Sphere = \dfrac{4}{3\:}\:pie\: r\³ }$

Let us Assume that the number of pellets of radius 1 cm that can be made from Solid  lead sphere of radius 8 cm is 'x'

Now,

$\bigstar$ Volume of solid lead sphere = x × volume of the spherical pellets.

$\implies$

$n*\dfrac{4}{3} pie\: r\³ = \dfrac{4}{3} pie\: R\³$

$\implies$

$n*\dfrac{4}{3} pie\: *1\³ = \dfrac{4}{3} pie\: *8\³$

• 4/3 and π get cancelled

$\implies$

n = 8³

{8³ = 512}

$\implies$

n = 512

$\red\bigstar$ Therefore , 512 spherical pellets each of radius 1 cm can be made from a solid lead sphere of radius 8 cm .