The diameter of Venus (from tables) is 12,100 km.
Therefore its radius is
r = 12100/2 = 6050 km = 6050 x 10³ m = 6.05 x 10⁶ m
The layer of gas is 50 km thick.
The outer radius of the surrounding layer of gas is
R = r + 50 x 10³ m
= 6.05 x 10⁶ + 50 x 10³ m
= 6.1 x 10⁶ m
The volume of the layer of gas is
V = [(4π)*3] * [(6.1 x 10⁶)³ - (6.05 x 10⁶)³] m³
= [(4π)/3] * 5.535875 x 10¹⁸ m³
= 2.318862 x 10¹⁹ m³
Because the density of the gas layer is 21 kg/m³, therefore the mass of the gas layer is
m = (21 kg/m³) * (2.318862 x 10¹⁹ m³)
= 4.8696 x 10²⁰ kg
Answer: [tex]4.8696 \times 10^{20} \, kg[/tex]
