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

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I am doing this question of mensuration which is very important for class 10 cbse board exam. In this question we have to find number of balls of radius 1cm formed from a sphere of radius 8 cm.

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 sphe re of radius 8 cm.