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.

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Solution

## Step 1: Find the volume of hemispherical bowlThe 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}$$⇒\frac{2}{3}×\frac{22}{7}×18×18×18=12219.43c{m}^{3}$Step 2: Find the height of cylindrical bottlesThe diameter of the cylindrical bottle$=6cm$The radius of the cylindrical bottle$=\frac{6}{2}=3cm$The volume of the one cylindrical bottle$={\mathrm{\pi r}}^{2}\mathrm{h}$$⇒\frac{22}{7}×3×3×\mathrm{h}=\frac{198}{7}\mathrm{h}$The volume of the $72$cylindrical bottle$=72×\frac{198}{7}h$If $10%$ of the liquid is wasted in this transfer, then $10%$ of $12219.43=\frac{10}{100}×12219.43=1221.943$The remaining volume of the liquid$=12219.43-1221.943=10997.487c{m}^{3}$$72×\frac{198}{7}h=10997.487⇒h=\frac{10997.487×7}{72×198}=5.4cm$Therefore, the height (h) of each bottle is $5.4cm$.

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