Universal Measuring Boxes with Triangular Bases

Measuring cups are everyday instruments used to measure the amount of liquid required for many common household tasks such as cooking. A measuring cup usually has gradations marked on its sides. In this paper we study measuring boxes without gradations which can nevertheless measure any integral amount, say liters, of liquid up to their full capacity. These boxes will be called universal measuring boxes. We study two types of measuring boxes with triangular bases, and for each type determine its maximum possible capacity.