How many solid spherical balls each of diameter 1.5 cm can be made by melting a solid cylinder with height 36 cm and base radius 8 cm?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4,096
Melting and recasting does not change the volume, so the number of balls is the volume of the cylinder divided by the volume of one ball.
Volume of the cylinder \(=\pi r^{2}h=\pi\times8^{2}\times36=2304\pi\,\mathrm{cm^{3}}\)
Radius of a ball \(=1.5\div2=0.75=\frac{3}{4}\) cm
Volume of a ball \(\displaystyle =\frac{4}{3}\pi\left(\frac{3}{4}\right)^{3}=\frac{4}{3}\times\frac{27}{64}\pi=\frac{9}{16}\pi\,\mathrm{cm^{3}}\)
Number of balls \(\displaystyle =2304\times\frac{16}{9}=4096\)