A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones.

For larger cylinder,

Height (H) = 5 cm

Radius (R) = 3 cm

For smaller cones,

Height (h) = 1 cm

Radius (r) = 1 mm = 0.1 cm

Let no. of smaller cones formed be n.

Volume of larger cylinder = n × Volume of smaller cones

$\Rightarrow π\text{R}^2\text{H} = \text{n} \times \dfrac{1}{3}π\text{r}^2\text{h} \\[1em] \Rightarrow \dfrac{22}{7} \times (3)^2 \times 5 = \text{n} \times \dfrac{1}{3} \times \dfrac{22}{7} \times (0.1)^2 \times 1 \\[1em] \Rightarrow \dfrac{22}{7} \times 9 \times 5 = \text{n} \times \dfrac{1}{3} \times \dfrac{22}{7} \times 0.01 \times 1 \\[1em] \Rightarrow \dfrac{990}{7} = \text{n} \times \dfrac{0.22}{21} \\[1em] \Rightarrow \text{n} = \dfrac{990 \times 21}{0.22 \times 7} \\[1em] \Rightarrow \text{n} = \dfrac{20790}{1.54} \\[1em] \Rightarrow \text{n} = 13500$

Hence, the number of cones formed = 13500.