¶ 2025 AMC 12B Problem 15
¶ Problem:
A container has a square bottom, a open square top, and four congruent trapezoidal sides, as shown. Starting when the container is empty, a hose that runs water at a constant rate takes minutes to fill the container up to the midline of the trapezoids. How many more minutes will it take to fill the remainder of the container?
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¶ Solution:
The midlines of each trapezoid form a square with side length . Extend the legs of each trapezoidal face to meet at a point , the vertex of the formed square pyramid. Consider , , and to be square pyramids with vertex and bases as the , , and squares respectively.
Suppose the volume of is . Since , , and are similar solids, we know the ratio of their volumes is their scale factor cubed. Therefore we may say that and .
The volume of water filled so far is and the volume of water left to be filled is . Since water fills proportionally to volume, we may find the number of minutes as minutes.
The problems on this page are the property of the MAA's American Mathematics Competitions