151k views
4 votes
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?

1 Answer

5 votes

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.

User Senerh
by
6.4k points