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A cylindrical rod of iron whose radius is one-fourth of its height is melted and cast into spherical balls of the same radius as that of the cylinder. What is the number of spherical balls ? 

(a) 2 

(b) 3 

(c) 4 

(d) 5

1 Answer

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(b) 3

Let the height of the cylindrical iron rod be h cm. Then, 

Radius of iron rod = Radius of spherical ball = \(\frac{h}{4}\) cm.

∴ Number of spherical balls = \(\frac{\text{Volume of cylindrical rod}}{\text{Volume of spherical ball}}\) 

= \(\frac{π\times\big(\frac{h}{4}\big)^2\times{h}}{\frac43\timesπ\times\big(\frac{h}{4}\big)^3}=3.\)

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