$\"\"$

The volume $\"\"$ of a hot-air balloon is $\"\"$ .

Radius of the balloon is $\"\"$ where $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Volume $\"\"$ of the balloon as a function of the time $\"\"$ is $\"\"$ where $\"\"$ .

$\"\"$

Surface area of the balloon as a function of the time $\"\"$ is $\"\"$ where $\"\"$ .