#### Answer

The reason for this is that when mixing around the formula PV = nRT for V=nRT/P and as you rise in the atmosphere both temperature and pressure decrease, however pressure will decrease at a faster and due to its inverse relationship with volume the balloon will gain volume.

#### Work Step by Step

Ground volume= (nR(293K))/101kpa)=2.901nR
this is STD for a volume (for simplicity n (moles) and R (the gas constant) are left as variables)
10km geometric altitude(volume)= (nR(220k))/27kpa) =8.14814nR
this is an equation for volume at a high above the earth at 10km where pressure is almost non existent but the temperature is still relatively high