. How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm?
Solution:
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.
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