The container shown below is made up of 2 cuboids and a 6-cm cube. The small cuboid has a square base of side 3 cm. The dimension of the big cuboid is 16 cm by 9 cm by 5 cm. There is 864 ml of water in the container and the height of the water level in the small cuboid and the cube is the same. What is the height of the water level from the base of the container? Answer: ___

1. Calculate the volume of the big cuboid at the base.

Volume of big cuboid $= 16 \times 9 \times 5 = 720 \text{ cm}^3$

2. Calculate the remaining volume of water that goes into the small cuboid and the cube.

Total volume of water $= 864 \text{ ml} = 864 \text{ cm}^3$
Remaining volume $= 864 - 720 = 144 \text{ cm}^3$

3. Calculate the combined base area of the small cuboid and the cube.

Base area of small cuboid $= 3 \times 3 = 9 \text{ cm}^2$
Base area of cube $= 6 \times 6 = 36 \text{ cm}^2$
Combined base area $= 9 + 36 = 45 \text{ cm}^2$

4. Calculate the height of the water level in the small cuboid and the cube, and then the total height from the base.

Height of water in upper parts $= 144 \div 45 = 3.2 \text{ cm}$
Total height from base $= 5 + 3.2 = 8.2 \text{ cm}$