Problem 12 · 2018 Math Kangaroo
Medium
Spatial & Visual Reasoning
spatial-reasoning
The five vases shown are filled with water at a constant rate. For which of the five vases does the graph shown describe the height of the water \(h\) as a function of the time \(t\)?
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Answer: D
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Hint 1 of 2
A constant fill rate means height rises fast where the vase is narrow and slowly where it is wide.
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Hint 2 of 2
Read the graph's changing slope and match it to a width profile.
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Approach: match the slope of h(t) to the cross-section width at each height
- The graph rises steeply at first, then flattens — the level climbs quickly low down and slowly higher up.
- Quick early rise means a narrow bottom; slowing rise means it widens going up.
- The cone standing on its point (narrow below, wide above) gives exactly this.
- Answer: (D).
Mark:
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