Yet another installment of puzzles...

[mendhak]

For a hot dog as the prize, what is the next number in this series?

341 444 533 602 705 848 1003 1098 1273 1420 .....


I'll give hints if you REALLY need it, and NO peeking!!


And here's another one for a hot dog AND a piece of NoteMe's ear:

My Dad has a miniature Pyramid of Egypt. It is 4 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1/ 3) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid? Give your answer to two places of decimal.