Question number three. A container in the shape of a cube needs to be filled with water. The area of its base is four decameters squared. A smaller cube-shaped container with the area of its base equal to one decameter squared is used to carry the water. At least how many trips with the smaller container are necessary to fill their larger container? I have drawn here a larger container and a smaller container, both in the shape of a cube, and so here the area of the base, let me shade in the base here, is four decameters squared. So that being a square, it has to measure two by two decameters. So let me just label that. And the smaller container, its base, is one decameter squared in area, so that has to be one decameter by one decameter, like that. And so now we see that the volume of the solid here is equal to two decameters, the length of one of the edges to the third power, so that's eight decameters cubed. And here the volume of the smaller container used to carry the water is one decameter cubed, and that comes out to exactly one decameter cubed. So if we were to use the smaller container to carry water and dump it into the larger container, this would take us exactly eight trips of one decameter cubed each. And so we have our answer. The volume of the larger container is eight times the volume of the smaller container, so it takes eight trips with the smaller container to fill up the larger container. And so the answer is 8d.

cube-shaped container

base area

cubic decameters

water filling

minimum trips