We divide the box into 3 sections, upper horizontal, middle horizontal and lower horizontal.

Part of the middle horizontal space is blocked by the cuboid.

Remaining unblocked length of the box's middle horizontal space
= 24cm - 4cm
= 20cm

The block is centred, so the remaining unblocked width and length of the middle horizontal space are divided equally into two sides.

For each side (left/right)
Remaining length = 20cm ÷ 2 = 10cm

10cm ÷ 3cm = 3 R 1cm
So the middle horizontal space can fit 3 cubes lengthwise on each side.


For the upper and lower horizontal spaces, they are unblocked lengthwise but blocked widthwise.

Remaining unblocked width of the box's upper and lower horizontal space combined = 18cm - 4cm = 14cm

Recall that the block is centred, so the remaining unblocked width and length are divided equally into two sides.

Now remaining unblocked width on each side of the upper and lower space
= 14cm ÷ 2 = 7cm

7 ÷ 3cm = 2 R 1cm

So the upper and lower horizontal space can fit 2 cubes widthwise each.

For lengthwise, there is no blockage so 24cm ÷ 3cm = 8. The two spaces each can fit 8 cubes lengthwise.


18cm ÷ 3cm = 6
The box can fit 6 cubes widthwise for areas that are not being blocked.

6 - 2 - 2 = 2

So the middle horizontal space can also hold 2 cubes widthwise , on each side.


Now we count the number of cubes.

For the upper and lower horizontal spaces, each space can fit 2 x 8 = 16 cubes.

The middle horizontal space can fit
2 x 3 = 6 cubes on each side.


For 1 layer of cubes , total number
= 16 + 16 + 6 + 6
= 44


Now the height is 9cm

9 cm ÷ 3cm = 3

This means we can stack 3 cubes and the top cube is flush with the top of the box.
Which means there can be 3 layers of cubes.


3 x 44 = 132

In total the box can fit 132 cubes.

Alternatively,


Without the cuboid blocking,

24cm ÷ 3cm = 8
18cm ÷ 3cm = 6

The box is able to fit 8 cubes lengthwise and 6 cubes widthwise.

8 x 6 = 48

For 1 layer, it would have been able to fit 48 cubes in one layer.


However, the cuboid's is obstructing the middle portion of the box.

Now its length and width measures 4cm x 4cm. This is the same across its height.

In the middl, there is a 6cm by 6cm space that's obstructed by this cuboid.

6cm ÷ 3cm = 2
It's able to fit 2 cubes lengthwise and 2 cubes widthwise.

2 x 2 = 4
So that space could have fitted 4 cubes without obstruction. But since there's the obstruction, 4 cubes have to be removed from the above calculation.

(You can divide the box into a 8 by 6 grid to see that there are a total of 48 cubes. And you will see a nice 2 x 2 square in the middle)


48 - 4 = 44


One layer fits 44 cubes. All layers in the cube experience the obstruction.


9cm ÷ 3cm = 3


The box can fit 3 cubes exactly heightwise.

So maximum number of cubes that can be fitted

= 3 layers x 44 per layer
= 132

thanks so much

Welcome