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.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 243.
Let the radius of the cylinder be r. Then, its height is 12r.
Volume of the cylinder = πr²h = πr²(12r) = 12πr³
Radius of each spherical ball = (1/3)r
Volume of one spherical ball = (4/3)π(1/3r)³ = (4/81)πr³
Number of spherical balls = (Volume of cylinder) / (Volume of one spherical ball)
= (12πr³) / [(4/81)πr³]
= 12 × (81/4)
= 243
Therefore, 243 spherical balls can be cast from the melted cylindrical rod.