Question

How many lead shots, each 3 mm in diameter, can be made from a cuboid with dimensions $12cm\times 11\times 9cm$?

Answer 1

now, you need to unify the units first and consider the data:

shots 3mm = 0.3cm we will need radius here not diameter therefore:
dia = 2r = 0.3cm
r = $\frac{0.3}{2}$ = 0.15cm

cuboid $12cm\times 11\times 9cm$
now, we need to calculate volumes of the cuboid as well as the shot

$a\times b\times hcm$​​​​​​​ = $12cm\times 11\times 9cm$​​​​​​​ = 1188cm3

$\frac{4\left(\pi \right)r^3}{3}$ = $\frac{4\times 3.14\times 0.15c{m}^3}{3}$​​​​​​​ = $0.01413c{m}^3$

we need now to divide cuboid volume by volume of the sphere:

$\frac{1188c{m}^3}{0.01413c{m}^3}$ = 84076.433

therefore from presented cuboid, after the roundup, you will make 84076 shots