Which has the greater density, a lake full of water or a cup full of lake water?

It should be the same.

Explanation:

The density is given by:

that means it depends on the mass and the volume occupied, so if the water is the same it doesn't matter the amount, it must be the same, the only way the density is not the same is in the case the lake water has other components that were no presented in normal water.

explanation:

could i give you a exaplo that could you?

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )