Problem 11 · 2019 Math Kangaroo
Medium
Geometry & Measurement
spatial-reasoning
The giants Tim and Tom build a sandcastle and decorate it with a flag. They push half the flagpole into the highest point of the sandcastle. The highest point of the flagpole is now 16 m above the floor, and the lowest is 6 m (see diagram). How high is the sandcastle?
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Answer: A — 11 m
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Hint 1 of 2
Find the whole length of the flagpole from its top and bottom heights.
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Hint 2 of 2
Half the pole is buried, so the sand reaches halfway up the pole; that halfway height is the castle.
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Approach: find pole length, then take the midpoint where the sand reaches
- The pole's top is 16 m up and its bottom is 6 m up, so the pole is 16 − 6 = 10 m long.
- Half the pole (5 m) is buried in the castle, starting from its bottom at 6 m.
- So the sand reaches up to 6 + 5 = 11 m, which is the top of the castle.
- The answer is A.
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