Question

mas force enco 6. A large raindrop (2500 pm = 2.5 mm radius) is 100 times the radius of a typical cloud droplet (25 um). How many times greater is its volume?

Answer 1

Given data:

Radius of larger raindrop,

`r_1=2.5\text{ mm}`

Radius of typical cloud droplet,

`r_2=25\text{ }\mu m`

Since, r1=100r2. Therefore,

`(r_1)/(r_2)=100`

The volume is given as,

`V=(4)/(3)\pi r^3`

Therefore, the volume of the large raindrop is,

`V_1=(4)/(3)\pi r^3_1`

The volume of the typical cloud is,

`V_2=(4)/(3)\pi r^3_2`

Taking ratios of the volume,

`\begin{gathered} (V_1)/(V_2)=((4)/(3)\pi r^3_1)/((4)/(3)\pi r^3_2) \\ =((r_1)/(r_2))^3 \end{gathered}`

Substituting all known values,

`\begin{gathered} (V_1)/(V_2)=(100)^3 \\ =10^6 \end{gathered}`

Therefore, the volume of the large raindrop equals 10^6 times the volume of a typical cloud droplet.