Pouring water between two containers

Tank A and Tank B are cubes. Tank A has an edge of thirty centimetres and is full of water. Tank B is empty. One tenth of the water in Tank A is poured into Tank B. The water heights in A and B are then in the ratio nine to four. Find the volume poured. Find the length of one edge of Tank B. Try it first. Pause if you like. Let us look at the same two tanks in depth. Before we calculate, watch the same amount of water on different bases. The same water, on a smaller base. What happens to its depth? Take a moment to predict. As the base gets smaller, the same water gets deeper. The amount of water stayed the same. Its base area and depth changed. Now return to Tank A and Tank B. The water that leaves A is exactly the water that enters B. First find the amount of water poured into B. For a cube, volume is length times breadth times height. One tenth times thirty times thirty times thirty gives the water poured. Cancel the ten in the denominator with the first thirty. The first thirty becomes three. The poured volume is two thousand seven hundred cubic centimetres. Because one tenth left Tank A, nine tenths remains. The water height in A is one minus one tenth, times thirty. That is twenty-seven centimetres. The question gives a ratio of the two water heights. Nine parts belong to the water height in A. Four parts belong to the water height in B. Nine units equal twenty-seven centimetres. One unit is twenty-seven divided by nine. That is three centimetres. Four units in B are four times three. That is twelve centimetres, the water height in B. We know how much water is in B and how deep it is. Dividing the volume by the depth tells us the area underneath. Base area equals volume divided by height. The water volume in B is two thousand seven hundred cubic centimetres. Its water height is twelve centimetres. Put that volume over that height to find the base area. The base area is two hundred and twenty-five square centimetres. Tank B is a cube, so its base is a square. The edge is the square root of that area. The length of B is the square root of two hundred and twenty-five square centimetres. That is fifteen centimetres. The same poured water has a different depth in B because it stands on a different square base. The volume is two thousand seven hundred cubic centimetres, and B has an edge of fifteen centimetres.