# Question

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

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

Thank you.

A wooden 125 cm³ is a solid cube that cannot be fitted into a space like liquid in any shape.

So you have to consider the maximum cubes that can be fitted into any sides of the container and in this case, 7 , 3 and 4 in  the direction of length , breadth and height.

I think even if the wooden cube is 1 cm³,   you can’t use straight division as the dimensions of the box may not be in integer like 10.1 cm. Possible scenario may be pouring fixed units of water of any volume to be fitted into a new space, then straight division can be used.