What is there to explain it self explanatory. What would happen if you threw a body into a lake of fire? Poof up in smoke it goes reduced to ash gone forever. The lake of fire is being consumed by God.
Your position of Hell as annihilation is a minority one and was not the prevalent understanding in Jesus' time. Here is a reference that explains:
Stewart D.F. Salmond, "Hell," in A Dictionary of the Bible, Dealing with its Language, Literature, and Contents, Including the Biblical Theology, edited by James Hastings, vol. 2 (Edinburgh: T. & T. Clark, 1898), pp. 343-46.
The most probable conclusion appears to be thisthat, while there were variations in belief from time to time, especially in the direction of annihilation, and divergent speculations in the Rabbinical schools, the idea generally connected with the term Gehenna, 'hell,' in our Lord's time was that of an irreversible doom for the wholly wicked, and that in His teaching as well as in that of His apostles the word was used in its popular and prevalent sense (see Schürer, History of the Jewish People II. ii. 183; Edersheim's Jesus the Messiah, ii. pp. 440, 791; Meyer, Commentary on Matthew 5:22; Holtzmann, Hand-Commentary on Matthew 5:22, Mark 3:29, 9:48).
Other terms are also used in the New Testament to express the penalty and the condition indicated by the word Gehenna, 'hell.' In the evangelical records of Christ's own discourses such terms are found employed as 'eternal fire'; 'unquenchable fire'; the place where 'their worm dieth not, and their fire is not quenched'; the 'prison' from which there is no coming out until 'the last farthing' is paid; 'eternal punishment' as contrasted with 'eternal life'; exclusion from the kingdom; banishment from Christ; 'weeping and wailing, and gnashing of teeth'; the 'outer darkness,' etc. (Matthew 18:8-9, Mark 9:43-49, Matthew 5:25-26, Luke 12:58-59, Matthew 25:46, 7:21-23, 13:42, 25:30). Elsewhere the final destiny of the unrighteous is described as 'the mist of darkness forever' (2 Peter 2:17); the 'blackness of darkness for ever' (Jude 13); the 'fierceness of fire' and 'perdition' (Hebrews 10:27, 39); 'great tribulation,' 'burning with fire,' being 'without,' the 'second death,' being cast into the 'lake of fire,' the 'lake that burneth with brimstone and fire' (Revelation 2:22-23; 18:8-9; 22:15; 2:11; 20:6, 14; 21:8; 20:10; 19:20); the 'wrath to come,' 'wrath and indignation, tribulation and anguish,' 'death,' 'punishment,' 'destruction,' 'eternal destruction from the face of the Lord' (Romans 2:5, 2 Thessalonians 1:9, Romans 2:8, 6:21, Philippians 3:19, 2 Thessalonians 1:9).