Volumes of revolution

There are 2 NRICH Mathematical resources connected to Volumes of revolution
Brimful
problem

Brimful

Age
16 to 18
Challenge level
filled star filled star empty star
Can you find the volumes of the mathematical vessels?
Brimful 2
problem

Brimful 2

Age
16 to 18
Challenge level
filled star empty star empty star
Which of these infinitely deep vessels will eventually full up?