Each cube's volume = 3cm x 3cm x 3cm
= 27cm³

Number of cubes in the diagram
= 15

Volume of figure = 15 x 27cm³
= 405cm³


For step 5, the last column has 5 cubes.

For step 4, the last column has 4 cubes.

For step 3, the last column has 3 cubes.

From this we see a pattern. The number of
cubes in the last column is always equal to the step number.

So there are 29 cubes in step 29.


So we need to add cubes for step 6 to step 29.


6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + ... + 26 + 27 + 28 + 29


From 6 to 29, there are 24 numbers
(29 number - first 5 numbers = 24)

Notice that :

6 + 29 = 35
7 + 28 = 35
8 + 27 = 35
...
...
15 + 20 = 35
16 + 19 = 35
17 + 18 = 35

We can pair up the numbers this way, and each pair is equal to 35.

Number of pairs
= 24 numbers ÷ 2 numbers per pair
= 12 pairs

12 x 35 = 420

420 more cubes are needed

Your second model in the second question is correct.

David has 2 units left and Benny has 3 unit left. Since they are equal, you should make the number of units the same.

The common multiple of 2 and 3 is 6.
2 x 3 = 6
3 x 2 = 6

Divide the units further to get 6 units for each boy.

Then add in the units that were spent and divide them the same way.

$23 average means the total is $23 x 2 = $46

Find the total number of units. Divide $46 by it to find how how much one unit is worth.

You can find David's spending easily from there