Question

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

Answer 1

let number of balls is x

thus

Vol. of x new balls  =  Vol. of  solid sphere
thus

4πr³/3 * x  = 4πR³/3

thus

r³ * x = R³
1³ * x = 8³
x = 512

Thus no. of balls formed is 512

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Answer 2

Radius of solid sphere = 8 cm
Volume = 4/3πr^3 = 4/3 x π x 8 x 8 x 8 cm^3

Radius of the ball = 2 cm
Volume of 1 ball = 4/3πr^3
= 4/3 x π x 2 x 2 x 2

Let the number of balls be X
X x 4/3 x π x 8 = 4/3 x π x 512
X x 8 = 512
X = 512/8
X = 64

Hence, number of required balls is 64

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