A rectangular water tank holds 216 liters of water. The depth is one-third of the length, and the breadth is half of one-third of the difference between the length and the depth. What is the length of the tank?

Explanation

Given the volume of 216 liters (which equals 2160 cubic decimeters), let the length be L dm. The depth is (1/3)L, and the breadth is half of one-third of (L - depth), which simplifies to (1/6)(L - (1/3)L) = (1/6)(2/3)L = (1/9)L. The volume formula is Length × Breadth × Depth = 2160. Substituting, we get L × (1/9)L × (1/3)L = 2160, which simplifies to (L^3) / 27 = 2160. Multiplying both sides by 27 gives L^3 = 58320. Taking the cube root, L = 18 dm.