Question

2. One cubic centimeter of a typical cumulus cloud contains 300 spherical liquid water drops, each with a typical radius of 10 um. For a certain spherical cumulus cloud with a radius of 2.0 km, what is the volume of liquid water that it contains? (Hint: first find the ratio of the volume of liquid water to the volume of cloud.)

Answer 1

Volume of spherical liquid drop
$v = \left ( \frac{4}{3} \right )\pi R^{3}$
where R is radius of spherical liquid drop = 10 *10^-6 m
On putting the value , we get
$v = \left ( \frac{4}{3} \right )\pi (10^{-5})^{3}$
v = 4.19*10^-15 m³
Now ,
Volume of 300 spherical liquid drop
V = 300v = 300*4.19*10^-15 = 1.257*10^-12 m³
Now it is given that the
1 Cm³ of cloud contain 300 Spherical liquid drop , therefore
Volume of liquid in 1 cm³ cloud = 1.257*10^-12 m³
10^-6 m³ of cloud = 1.257*10^-12 m³ of liquid
1 m³ of cloud = 1.257*10^-6 m³ of liquid
Now the volume of cloud of radius (r) = 2 km = 2000 m
Volume of cloud
$V_{c} = \left ( \frac{4}{3} \right )\pi (r)^{3}$
$V_{c} = \left ( \frac{4}{3} \right )\pi (2000)^{3}$
V_C = 33.51*10⁹ m³
Now volume of liquid in cloud will be
$V_{L} = 33.51*10^{9}*1.257*10^{-6}$
V_L = 42.12*10³ m³
hence the volume of liquid in spherical cumulus cloud would be 42.12*10³ m³