A solid lead cylinder of height 45 m and radius 36 cm is melted and made into spherical bullets, each of diameter 4.5 cm. How many bullets can be made?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3,84,000
Melting does not change the volume, so number of bullets \(=\) volume of the cylinder \(\div\) volume of one bullet. Both volumes contain \(\pi\), so it cancels. All lengths must be in the same unit.
Height of the cylinder \(=45\) m \(=4500\) cm; radius of a bullet \(=4.5\div2=2.25\) cm
Volume of the cylinder \(=\pi\times36^2\times4500=5832000\,\pi\) cm3
Volume of one bullet \(\displaystyle=\frac{4}{3}\pi\times2.25^3=15.1875\,\pi\) cm3
Number of bullets \(=5832000\div15.1875=3{,}84{,}000\)