How many lead shots each 0.3 cm in diameter can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm?

1. 7200

2. 8400

3. 72000

4. 84000

Shots is in the shape of sphere.

Radius of sphere, r = $\dfrac{\text{diameter}}{2} = \dfrac{0.3}{2} = 0.15 \text{cm.}$

Let the number of spheres formed be n.

Volume of cuboid = n × Volume of each lead shot

$\therefore \text{lbh} = \text{n} \times \dfrac{4}{3} π \text{r}^3 \\[1em] \Rightarrow 9 \times 11 \times 12 = \text{n} \times \dfrac{4}{3} \times \dfrac{22}{7} \times 0.15^3 \\[1em] \Rightarrow 1188 = \text{n} \times \dfrac{4}{3} \times \dfrac{22}{7} \times 0.003375 \\[1em] \Rightarrow 1188 = \text{n} \times \dfrac{0.297}{21} \\[1em] \Rightarrow \text{n} = \dfrac{21 \times 1188}{0.297} \\[1em] \Rightarrow \text{n} = \dfrac{24948}{0.297} \\[1em] \Rightarrow \text{n} = 84000.$

Hence, option 4 is the correct option.