Radius of cylinder, r = 3.5 cm
Height, h = 14cm
Volume of cylinder,
V = πr2h
= π x (3.5)2 x 14
= 171.5 π
Radius of the ball, r = \(\frac 7{12}\) cm
Volume of sphere,
V \(= \frac 43 \pi r^3\)
\(= \frac 43 \pi \times \left(\frac 7{12}\right)^3\)
\(= \frac{343}{1296} \pi \)
\(= 0.2646π\)
Number of balls made,
\(n = \frac{\text{Volume of cylinder}}{\text{Volume of sphere}}\)
\(= \frac{171.5 \pi}{0.2646 \pi}\)
\(= 648.148\)
Hence, the total number of metallic balls that can be formed is 648.