Volume mixed-practice questions

A tank with a square base is 20 centimetres high. Here's the tank. It contains 2.7 litres of water, and the water stands 12 centimetres deep. Find the length of one side of the base. The base itself has no number on it. Try it first. Pause if you like. The answer we want is a length, in centimetres. What we're given is an amount of water, and a depth. The rule that ties those together is this one. Volume is length, times breadth, times height. The water is measured in litres, and the tank is measured in centimetres. One litre is one thousand millilitres, so 2.7 litres is two thousand, seven hundred millilitres. And one millilitre of water fills exactly one cubic centimetre. The water is a box of its own. Its floor is the tank's floor. And its height is the 12 centimetres the water stands at, not the 20 centimetres the tank is. Length times breadth is the floor of the tank. So we divide the water's volume by its own depth. Two thousand, seven hundred divided by 12 is two hundred and twenty five. And cubic centimetres, divided by centimetres, leaves square centimetres. Cut one layer off the water, one centimetre thick. The top of that layer is the floor, and its area is the two hundred and twenty five square centimetres. The base is a square, so its two sides are the same number. One side of a square floor is the square root of its area. 15 times 15 is two hundred and twenty five, so one side of the base is 15 centimetres. A volume is a base area, stacked. Share it over the layers, and what comes back is the base area. The side of a square base is the square root of its area. Cubic centimetres means a volume, square centimetres means a floor area, and centimetres means a side.