Half a barrel is 50%. Pour out 40% of it, and the remaining proportion is: 50%x( 1-40%)=30%.

30% is 24 liters, so the total volume is 24÷30%=80 liters.

80 liters =80 cubic decimeters

Volume = bottom area x height

Height = volume/bottom area

=80÷ 10

=8 decimetres

The barrel height is 8 decimeters.

Please adopt it if it is helpful, and ask if you don't understand it. Thank you.