NumericalModerate3 marks
A solid spherical ball of radius 6 cm is melted and recast into 64 identical spherical marbles. Find the radius of each marble.
Topic: Mensuration of solids
Previous-year question practice database
Answer
Exam answer
Radius of the original spherical ball: R = 6 cm
Let the radius of each marble be r cm.
Volume of original sphere:
V = (4/3)πR³
= (4/3)π(6)³
= (4/3)π(216)
= 288π cm³
There are 64 identical marbles.
Volume of 64 marbles:
64 × (4/3)πr³
Since the original ball is melted and recast, volume is conserved:
64 × (4/3)πr³ = 288π
64r³ = 216
r³ = 216/64
= 27/8
r = 3/2
= 1.5 cm
Answer:
Radius of each marble = 1.5 cm.
Explanation
Melting and recasting conserve volume. Therefore the volume of the original sphere equals the combined volume of the 64 smaller spheres; the common factor (4/3)π cancels.
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