A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.

Given,

Height of large cylindrical vessel (h₁) = 24 cm

Diameter of large cylindrical vessel = 40 cm

Radius of large cylindrical vessel (r₁) = $\dfrac{40}{2}$ = 20 cm.

Height of small cylindrical vessel (h₂) = 10 cm

Diameter of small cylindrical vessel = 8 cm

Radius of small cylindrical vessel (r₂) = $\dfrac{8}{2}$ = 4 cm.

Let no. of small cylindrical bottles which can be filled be n.

Volume of large cylindrical vessel = n × Volume of small cylindrical vessel

$\therefore \dfrac{1}{3}πr$1^2h1 = n \times \dfrac{1}{3}πr2^2h2 \\[1em] \Rightarrow n = \dfrac{r1^2h1}{r2^2h2} \\[1em] \Rightarrow n = \dfrac{20^2 \times 24}{4^2 \times 10} \\[1em] \Rightarrow n = \dfrac{400 \times 24}{16 \times 10} \\[1em] \Rightarrow n = 60.

Hence, no. of small cylindrical bottles which an be filled = 60.