Question

How many spherical balls of radius 1 cm can be made by melting a hemisphere of radius 6 cm?

Answer 1

diameter of hemisphere [D]=6 cm ∴ R=3 cm

diameter of spherical balls [d]=1 cm ∴ r=1/2 cm

Let no. of lead balls be 'n'

Vol. of sphere = n x Vol of 1 lead ball

4/3 pi R3 = n x 4/3 pi r3

⇒4/3 pi R3 = n x 4/3 pi r3

⇒3 x 3 x 3 = n x 1/2 x 1/2 x 1/2

⇒27 x 8 = n

Therefore, n = 216 lead balls. ANS

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Answer 2

Let n number of spherical balls of radius 1 cm can be made

so  Volume of hemisphere = n × volume of 1 spherical balls

⇒4/3 π × R^3 = n × 4/3 π r^3

⇒(6)^3 = n× (1)^3

So n=216

216 small sphere ball can be made