Question

A hemispherical bowl of internal diameter $36cm$ contains liquid. This liquid is filled into $72$ cylindrical bottles of diameter $6cm$. Find the height of each bottle, if $10\%$ liquid is wasted in this transfer.

Answer 1

Step 1: Find the volume of hemispherical bowl

The internal diameter of the hemispherical bowl$=36cm$

The internal radius of the hemispherical bowl$=\frac{36}{2}=18cm$(Radius is half of the diameter)

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

$\Rightarrow \frac{2}{3}\times \frac{22}{7}\times 18\times 18\times 18=12219.43c{m}^3$

Step 2: Find the height of cylindrical bottles

The diameter of the cylindrical bottle$=6cm$

The radius of the cylindrical bottle$=\frac{6}{2}=3cm$

The volume of the one cylindrical bottle$={\mathrm{\pi r}}^2\mathrm{h}$

$\Rightarrow \frac{22}{7}\times 3\times 3\times \mathrm{h}=\frac{198}{7}\mathrm{h}$

The volume of the $72$cylindrical bottle$=72\times \frac{198}{7}h$

If $10\%$ of the liquid is wasted in this transfer, then $10\%$ of $12219.43=\frac{10}{100}\times 12219.43=1221.943$

The remaining volume of the liquid$=12219.43-1221.943=10997.487c{m}^3$

$72\times \frac{198}{7}h=10997.487\Rightarrow h=\frac{10997.487\times 7}{72\times 198}=5.4cm$

Therefore, the height (h) of each bottle is $5.4cm$.