Question

A hemispherical bowl of internal radius 12 cm contains some liquid. This liquid is to be filled into cylindrical bottles of diameter 4 cm and height 6 cm. How many bottles can be filled with this liquid?

Answer 1

We know, volume of hemisphere (v)=$\frac{2}{3} \pi r^{3}$

where, r is radius = 0.12m

hence, v = $2.304*10^{-3} \pi$

Volume of cylindrical bottle(u)=$\pi R^{2} h$

where,R=0.02m is the radius of cylinder and h=0.06m is height.

hence, u =$2.4*10^{-5} \pi$

Let,n is the number of bottle filled,

hence n = $\frac{v}{u}$

= 96

Answer 2

Dear Student,

Answer: 84 bottles

Solution:

How much liquid that hemisphere contained is calculated by the volume formula.

We know that volume of Hemisphere,with radius r is given as
$\frac{2}{3} \pi {r}^{3} \\ \\ \pi = 3.141 \\ \\ r = 12 \: cm \\ \\ volume \: = \frac{2}{3} \times 3.141 \times ( {12)}^{3} \\ \\ = \frac{2}{3} \times 3.141 \times 1728 \\ \\ = 6336\: \: {cm}^{3}$
Now to find the capacity of cylindrical bottles,

calculate the Volume of bottles

given as
$= \pi {r}^{2} h \\ \\ = \frac{22}{7} \times ( {2)}^{2} \times 6 \\ \\ = \frac{22 \times 4 \times 6}{7} \\ \\ = 75.42 \: \: {cm}^{3}$
Total number of bottles filled= Volume of hemisphere/ volume of bottle

=
$\frac{6336}{75.42 } \\ \\ = 84 \: \: bottles$
Hope it helps you