Question

A spherical weather balloon is constructed so that the gas inside can expand as the balloon ascends to higher altitudes where the pressure is lower. If the radius of the spherical balloon is 3m at sea level where the pressure is 1.0 x 105 Pa, what will be the radius at an altitude of about 10 km where the pressure of the gas is 2.16 x 104 Pa? For simplicity, assume the temperature has not changed. ​

Answer 1

Dear student
volume of a sphere: V = (4/3)(π)(r³).
Let the required radius be x

Using
​P₁V₁ = P₂V₂ for this:
[(4/3)(3.14159)(3 m)³] (1.0 x 10⁵ Pa) = [(4/3)(3.14)(x)³] (2.16 x 10⁴ Pa)

Here the (4/3)(π) portion will cancel out:
(3m)³ (1.0 x 10⁵ Pa) = (x)³ (2.16 x 10⁴ Pa)
x³ = [(27 m³) (1.0 x 10⁵ Pa)] / 2.16 x 10⁴ Pa
x³ = 125 m³
x = 5 m

Regards