How to find a volume of this figure (which is $3080 \text{ cm}^3$) in a few seconds?

Question

I was watching this Japanese game show and came across this question:

The contestants were told that each small cube is 2cm on its side and were asked to find the volume of the above figure.

The answer was 3080 $cm^3$.

While I was counting the number of cubes for the first row, one of the contestants was able to answer this within a few seconds.

I'm curious about how he did it. I assumed the figure was constructed in some sort of pattern and was hoping someone could shed some light on this.

(The game show didn't explain how to solve this unfortunately...)

Answer 1

I looked at the horizontal layers.

Top layer has seven, and each layer below shows seven more. So the number of cubes is $$ 7+14+\cdots+70=\frac{77}2\cdot10=385\,. $$

Answer 2

So we start on the left, and kind of slice it diagonally, if it makes sense.

The first diagonal layer has TWO columns, one with $2$ blocks and another with $2$ blocks.

The second diagonal layer has THREE columns, one with $4$ blocks, another with $3$ blocks, and another with $3$ blocks.

The third diagonal layer has FIVE columns, with $6$, $4$, $2$, $2$ and $1$ blocks.

If we sum it up to the tenth diagonal layer, we end up with a total of $385$ blocks.

EDIT: Didn't see the pattern.

Answer 3

Here's my idea for how someone could answer this in a few seconds.

1. See that there are ten horizontal layers
2. See that each layer adds seven blocks
3. Know that the tenth triangular number is $55$.
4. Know that $2 ^ 3 = 8$
5. Multiply $8 \cdot 55 \cdot 7$