Question

A metal sphere of radius 20 cm is melted and then cast into small hemispheres each of radius 5 cm. Find the number of hemispheres thus obtained.
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Answer 1

QuestioN :

A metal sphere of radius 20 cm is melted and then cast into small hemispheres each of radius 5 cm. Find the number of hemispheres thus obtained.

GiveN :

• A metal sphere of radius 20 cm is melted and then cast into small hemispheres each of radius  5 cm.

To FiNd :

• The number of hemispheres thus obtained.

ANswer :

∴ Number of hemispheres obtained = 128.

SolutioN :

Radius of sphere = 20 cm

Radius of small hemisphere = 5 cm

Now, let the number of small hemispheres obtained be 'n'

Now we know,

Volume of sphere = 4/3 πr³

Volume of hemisphere = 2/3 πr³

Now atq,

⇒ Volume of sphere = n * Volume of hemispheres

⇒ 4/3 π(20)³ = n × 2/3 π(5)³

⇒ 4/3 π * 8000 = n × 2/3 π × 125

⇒ 2 * 8000 = n × 125

⇒ 16000 = 125n

⇒ n = 16000/125

⇒ n = 128

∴ Number of hemispheres obtained = 128.