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?

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Solution

## Step 1: Find the volume of the hemispherical bowlThe radius of the hemispherical bowl$=9cm$The volume of the hemispherical bowl$=\frac{2}{3}\pi {r}^{3}$$=\frac{2}{3}×\frac{22}{7}×9×9×9=1527.42c{m}^{3}$Step 2: Find the volume of the cylindrical-shaped bottleThe radius of the cylindrical-shaped bottles$=\frac{3}{2}=1.5cm$(Radius is half of the diameter)The height of the cylindrical-shaped bottles$=4cm$The volume of the cylindrical-shaped bottles$=\pi {r}^{2}\mathrm{h}$$=\frac{22}{7}×1.5×1.5×4=28.28{\mathrm{cm}}^{3}$Step 2: Find the number of the cylindrical-shaped bottleLet n bottles are needed, so the volume of n cylindrical bottles$=28.28×n$$⇒28.28×n=1527.42\phantom{\rule{0ex}{0ex}}⇒n=\frac{1527.42}{28.28}\phantom{\rule{0ex}{0ex}}⇒n=54$Hence, the number of bottles required is $54$.

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