A cylindrical rod of iron whose height is twelve times its radius, is melted and cast into spherical balls, each of one-third the radius of the cylinder. Find the number of spherical balls.
A.243✓ Correct
B.212
C.224
D.198
Explanation
Let cylinder radius = r, height = 12r. Volume of cylinder = πr²×12r = 12πr³. Each ball has radius r/3, volume = (4/3)π(r/3)³ = 4πr³/81. Number of balls = 12πr³ ÷ (4πr³/81) = 12 × 81/4 = 243.
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