Given data:
Radius of larger raindrop,
[tex]r_1=2.5\text{ mm}[/tex]Radius of typical cloud droplet,
[tex]r_2=25\text{ }\mu m[/tex]Since, r1=100r2. Therefore,
[tex]\frac{r_1}{r_2}=100[/tex]The volume is given as,
[tex]V=\frac{4}{3}\pi r^3[/tex]Therefore, the volume of the large raindrop is,
[tex]V_1=\frac{4}{3}\pi r^3_1[/tex]The volume of the typical cloud is,
[tex]V_2=\frac{4}{3}\pi r^3_2[/tex]Taking ratios of the volume,
[tex]\begin{gathered} \frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r^3_1}{\frac{4}{3}\pi r^3_2} \\ =(\frac{r_1}{r_2})^3 \end{gathered}[/tex]Substituting all known values,
[tex]\begin{gathered} \frac{V_1}{V_2}=(100)^3 \\ =10^6 \end{gathered}[/tex]Therefore, the volume of the large raindrop equals 10^6 times the volume of a typical cloud droplet.
