A solid cone of radius 5 cm and height and height 9 cm is melted and made into small cylinders of radius 0.5 cm and height 1.5 cm. Find the number of cylinders so formed.

Let number of small cylinders formed be n.

Given,

Radius of cone (R) = 5 cm,

Height of cone (H) = 9 cm,

Radius of cylinder (r) = 0.5 cm,

Height of cylinder (h) = 1.5 cm

Since, cone is melted and recasted into n cylinders.

∴ Volume of cone = n × Volume of sphere

$\Rightarrow \dfrac{1}{3}πR^2H = n \times πr^2h\\[1em] \Rightarrow \dfrac{1}{3} \times \dfrac{22}{7} \times 5^2 \times 9 = n \times \dfrac{22}{7} \times (0.5)^2 \times 1.5\\[1em] \Rightarrow \dfrac{1}{3} \times \dfrac{22}{7} \times 25 \times 9 = n \times \dfrac{22}{7} \times 0.25 \times 1.5\\[1em] \Rightarrow \dfrac{1}{3} \times 25 \times 9 = n \times 0.25 \times 1.5\\[1em] \Rightarrow 25 \times 3 = n \times 0.25 \times 1.5\\[1em] \Rightarrow 75 = 0.375n\\[1em] \Rightarrow n = \dfrac{75}{0.375}\\[1em] \Rightarrow n = 200.$

Hence, number of cylinders formed = 200.