A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and diameter 1 cm. Find the number of cones formed.

For larger cone,

Height (h₁) = 8 cm

Radius (r₁) = 6 cm

For smaller cones,

Height (h₂) = 2 cm

Radius (r₂) = $\dfrac{1}{2}$ = 0.5 cm

Let no. of smaller cones be n.

Volume of larger cone = n × Volume of smaller cones

$\Rightarrow \dfrac{1}{3}πr$1^2h1 = n \times \dfrac{1}{3}πr2^2h2 \\[1em] \Rightarrow r1^2h1 = n \times r2^2h2 \\[1em] \Rightarrow n = \dfrac{r1^2h1}{r2^2h2} \\[1em] \Rightarrow n = \dfrac{6^2 \times 8}{(0.5)^2 \times 2} \\[1em] \Rightarrow n = \dfrac{288}{0.5} \\[1em] \Rightarrow n = 576.

Hence, no. of cones formed = 576.