# A hemispherical bowl of internal radius 9 cm is full of liquid.

Question:

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?

Solution:

The internal radius of the hemispherical bowl is 9cm. Therefore, the volume of the water in the hemispherical bowl is

$V=\frac{2}{3} \pi \times(9)^{3} \mathrm{~cm}^{3}$

The water in the hemispherical bowl is required to transfer into the cylindrical bottles each of radius $\frac{3}{2} \mathrm{~cm}$ and height $4 \mathrm{~cm}$. Therefore, the volume of each of the cylindrical bottle is

$V_{1}=\pi \times\left(\frac{3}{2}\right)^{2} \times 4 \mathrm{~cm}^{3}$

Therefore, the required number of cylindrical bottles is

$\frac{V}{V_{1}}=\frac{\frac{2}{3} \pi \times(9)^{3}}{\pi \times\left(\frac{3}{2}\right)^{2} \times 4}$

$=\frac{2 \times(9)^{3} \times(2)^{2}}{3 \times(3)^{2} \times 4}$

$=54$

Hence No. of bottles $=54$