Question
Download Solution PDFAn iron ball of radius 21 cm is melted and recast into spherical balls of radius 7 cm. Find the number of spherical balls.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven data:
Radius of the large iron ball = 21 cm
Radius of the small spherical balls = 7 cm
Concept Used:
The volume of a sphere is (4/3)πr³.
The number of small balls that can be formed from a larger ball is the ratio of their volumes,
because volume is conserved when the iron ball is melted and recast.
Calculation:
⇒ Volume of the large iron ball = (4/3)π × (21)³
⇒ Volume of a small spherical ball = (4/3)π × (7)³
Number of small balls = (Volume of the large ball)/(Volume of a small ball) = (21/7)³ = 27
Therefore, 27 spherical balls of radius 7 cm can be formed.
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