You are using water to dilute small amounts of chemicals in the laboratory, drop by drop. How many drops of water are in a $\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{-}\mathit{L}$ bottle? (Hint: Start by estimating the diameter of a drop of water.)

Here,

As in the question hint is given to estimate the diameter of the drop of water. Once you suppose the diameter of water to be a number we can find out radius by dividing it with two.

Water droplets are always considered in form of a sphere hence the diameter of sphere will be getting.

Using the radius of the sphere we can find out the volume of water present in one drop of water.

D= diameter of water droplet (in)

R= radius of water droplet (in)

V= Volume of water droplet ($i{n}^3$)

Volume of sphere can be obtained by multiplying the radius cube to the value of pie and $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

Let suppose the diameter of water droplet be $0.16$inch. Hence the radius of the drop will be $R=0.08$inch

Volume of water droplet =$\begin{array}{rcl}V& =& \frac{4}{3}{\mathrm{\pi R}}^3\\ & =& \frac{4}{3}\mathrm{\pi }{\left(0.08\right)}^3\\ & =& 0.0021{\mathrm{in}}^3\end{array}$

The volume of one droplet is $0.0021{\mathrm{in}}^3$.

Again, we need to do conversion here in this case. The number of drops in one liter of bottle can be calculated as below:

$$\begin{gathered} =\frac{1drop}{0.021i{n}^3}\times {\left(\frac{1in}{2.54cm}\right)}^3\times \left(\frac{1000c{m}^3}{1L}\right) \\ =29058.925droplets/L \end{gathered}$$

Therefore, after the experiment calculation we got around $29058.925$drops of water in the bottle per liter.