When would someone need to use area and volume in real life

real life situations.............. one example for area and one for volume.

Area: how much carpet you want to put in your house
Volume: how large you want to build a swimming pool

Engineering is a prime example of what you are wanting to know. I like answering this question with an example of an air compressor tank. Volume would vary directly with area. The bigger the air tank the higher the volume of air it could hold. This is not counting the pressure the air inside the tank.

If you needed to install 3" of loam in your 100' x 100' yard it would be nice to know it's area
and the volume of loam needed so you don't get ripped off. If you had no idea how to figure it I
would love to be the contractor billing for your materials that were delivered.

Area: Amount of paint you need to paint the walls.

Volume: How much concrete you need to order to pour your driveway.