Question

A hemispherical bowl of internal radius $9cm$ contains a liquid. This liquid is to be filled into cylindrical-shaped small bottles of diameter $3cm$ and height $4cm$. How many bottles will be needed to empty the bowl?

Answer 1

Step 1: Find the volume of the hemispherical bowl

The radius of the hemispherical bowl$=9cm$

The volume of the hemispherical bowl$=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\times \frac{22}{7}\times 9\times 9\times 9=1527.42c{m}^3$

Step 2: Find the volume of the cylindrical-shaped bottle

The radius of the cylindrical-shaped bottles$=\frac{3}{2}=1.5cm$(Radius is half of the diameter)

The height of the cylindrical-shaped bottles$=4cm$

The volume of the cylindrical-shaped bottles$=\pi r^2\mathrm{h}$

$=\frac{22}{7}\times 1.5\times 1.5\times 4=28.28{\mathrm{cm}}^3$

Step 2: Find the number of the cylindrical-shaped bottle

Let n bottles are needed, so the volume of n cylindrical bottles$=28.28\times n$

$$\begin{gathered} \Rightarrow 28.28\times n=1527.42 \\ \Rightarrow n=\frac{1527.42}{28.28} \\ \Rightarrow n=54 \end{gathered}$$

Hence, the number of bottles required is $54$.