A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?

Given,

Internal radius of hemispherical bowl (R) = 9 cm

Diameter of each conical container = 3 cm

So, radius (r) = $\dfrac{3}{2}$ = 1.5 cm and height of conical container(h) = 4 cm

Let no. of conical containers needed be n.

∴ Volume of hemispherical bowl = n × Volume of each conical shaped container

$\Rightarrow \dfrac{2}{3}πR^3 = n \times \dfrac{1}{3}πr^2h \\[1em] \Rightarrow n = \dfrac{\dfrac{2}{3}πR^3}{\dfrac{1}{3}πr^2h} \\[1em] \Rightarrow n = \dfrac{2 \times (9)^3 \times 3}{1 \times (1.5)^2 \times 4 \times 3} \\[1em] \Rightarrow n = \dfrac{2 \times 729 \times 3}{2.25 \times 4 \times 3} \\[1em] \Rightarrow n = 162.$

Hence, 162 containers are necessary to empty the bowl.