2025 AMC 10B Problem 19
Problem 19 of 25HarderGeometry
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?
Answer choices
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Solution
The container is a square frustum: a horizontal slice at height fraction has side Extend the sides up to their apex, and the volume out to where the side length is scales as So the whole container is parts, the piece up to the midline (side ) is parts, and the rest is parts. Those parts take minutes, so each part is minutes. The remaining parts take minutes. Thus, D is the correct answer.