### Three Cubes

Can you work out the dimensions of the three cubes?

### Concrete Calculation

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?

### In a Spin

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

# Maths Filler 2

##### Stage: 4 Challenge Level:

The first 6 marks are filled one every half minute.

Then for mark 7 we first fill up to 6 completely:

$M+ = 1+3+1 = 5$
$A+ = \frac{3.5+4}{2} \times 2 +4 - \frac{1+2}{2} \times 2 +2 = 10.5$
$T+ = 6+2 = 8$
$H+ = 3+3+3+1 = 10$
$S = 4+1+1+1+1+0.5 = 8.5$
42 total

And then fill up to 7:

$M = 2$
$A = \frac{3.5 + 3.375}{2} \times 0.5 -1 \times 0.5 = \frac{39}{32}$
$T = 2$
$H = 2$
$S = 2 \times \frac{1}{2} + \frac{1}{8} = \frac{9}{8}$

$\frac{267}{32}$ total (sum to this point = $\frac{1707}{32}$)

And following the same process for the rest of the levels:

Level 8: $\frac{225}{32}$ total (sum to this point = $\frac{1932}{32}$)

level 9: $\frac{267}{32}$ total (sum to this point = $\frac{2199}{32}$)

Level 10: $\frac{249}{32}$ total (sum to this point = 76.5)

The sum of all these is 76.5.

Now if we check the total size to check it's the same: $24 \times 5 - 23.5 \textrm{ spaces} = 76.5$ check!

So we can plot these points on a graph! Joining them up is another matter...