A container is in the shape of a cuboid - Edexcel - GCSE Maths - Question 5 - 2019 - Paper 2

Since the container is (\frac{2}{3}) full, the volume of water is:

$V_{water} = \frac{2}{3} \times 3420 \text{ cm}^3 = 2280 \text{ cm}^3$

Note that 1 cm³ equals 1 ml. Therefore, we have: $V_{water} = 2280 \text{ ml}$

To find the number of cups that can be filled, we divide the total volume of water by the volume of one cup:

$\text{Number of cups} = \frac{2280 \text{ ml}}{275 \text{ ml/cup}} \approx 8.29$

As we can only fill whole cups, the greatest number of cups that can be completely filled is 8.