A hollow cylindrical drum has internal diameter of 30 cm and a height of 1 m. What is the maximum number of cylindrical boxes of diameter 10 cm and height 10 cm each that can be packed in the drum?

1. 60

2. 70

3. 80

4. 90

In hollow cylindrical drum,

Height, H = 1 m = 100 cm

Radius, R = $\dfrac{\text{Diameter}}{2} = \dfrac{30}{2}$ = 15 cm

For each cylindrical boxes,

Height, h = 10 cm

Radius, r = $\dfrac{\text{Diameter}}{2} = \dfrac{10}{2}$ = 5 cm

Let the maximum number of cylindrical boxes that can be packed be n.

Volume of hollow cylinder = n × Volume of cylindrical box

$\therefore π\text{R}^2\text{H} = \text{n} \times π\text{r}^2\text{h} \\[1em] \Rightarrow \text{R}^2\text{H} = \text{n} \times \text{r}^2\text{h} \\[1em] \Rightarrow 15^2 \times 100 = \text{n} \times 5^2 \times 10 \\[1em] \Rightarrow 225 \times 100 = \text{n} \times 25 \times 10 \\[1em] \Rightarrow 22500 = \text{n} \times 250 \\[1em] \Rightarrow \text{n} = \dfrac{22500}{250} \\[1em] \Rightarrow \text{n} = 90.$

Hence, option 4 is the correct option.