What is the maximum number of 5-cm cubes that I can cut from a wooden block measuring 35cm by 17cm by 23cm?

Vol. of wooden block = 35 cm x 17 cm x 23 cm = 13685 cm3

Vol. of 1 cube = 5 cm x 5 cm x 5 cm = 125 cm3

13685 ÷ 125 = 109.48, so maximum number is 109.

However, correct solution is:

No. of cubes along 35 cm = 35 cm ÷ 5 cm = 7

No. of cubes along 17 cm = 17 cm ÷ 5 cm = 3 R 2cm

No. of cubes along 23 cm = 23 cm ÷ 5 cm = 4 R 3cm

Max no. of cubes = 7 x 3 x 4 = 84

- Anyone can explain, especially, why 7 cubes x 3 cubes x 4 cubes?
- And what kind of word problem a method like vol of wooden block ÷ vol. of 1 cube would be use?

Thank you.