A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm.
Question:

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

Solution:

Internal radius of the hemispherical bowl = 9 cm
Radius of a cylindrical shaped bottle = 1.5 cm
Height of a bottle = 4 cm

Number of bottles required to empty the bowl $=\frac{\text { volume of the hemispherical bowl }}{\text { volume of a cylindrical shaped bottle }}$

$=\frac{\frac{2}{3} \pi \times 9^{3}}{\pi \times 1.5^{2} \times 4}$

$=\frac{2 \times 9 \times 9 \times 9}{3 \times 1.5 \times 1.5 \times 4}$

$=54$

∴ 54 bottles are required to empty the bowl.

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