How many lead shots each 3 cm in radius can be made by melting a solid cuboid of dimensions 9 cm × 22 cm × 12 cm?
(Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 21
Melting and recasting does not change the amount of metal, so the number of shots = volume of the cuboid ÷ volume of one shot. Each shot is a sphere of radius 3 cm.
Volume of the cuboid \(=9\times22\times12=2376\,\mathrm{cm^3}\)
Volume of one shot \(\displaystyle =\frac{4}{3}\pi r^3=\frac{4}{3}\times\frac{22}{7}\times27=\frac{792}{7}\,\mathrm{cm^3}\)
Number of shots \(\displaystyle =2376\div\frac{792}{7}=\frac{2376\times7}{792}=3\times7=21\)