Problem 17 · 1990 AJHSME
Hard
Geometry & Measurement
volumeunit-conversionround-up
A straight concrete sidewalk is to be 3 feet wide, 60 feet long, and 3 inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?
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Answer: A — 2.
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Hint 1 of 2
The mixed units (feet and inches) are the first trap — get everything into the *same* unit before multiplying. 3 inches is what fraction of a foot?
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Hint 2 of 2
Two more traps after the volume: 1 cubic yard is 3×3×3 = 27 cubic feet (not 3), and 'must order a whole number' means round UP, never down — you can't buy 1.67 yards of concrete.
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Approach: match units, find volume, convert with 27, round up
- Convert the odd one out: 3 inches = 3/12 = 1/4 foot. Now all three measurements are in feet: 3 ft wide, 60 ft long, 1/4 ft thick.
- Volume = 3 × 60 × 1/4 = 45 cubic feet.
- A cubic yard is a 3 ft cube, so it holds 3×3×3 = 27 cubic feet (the easy mistake is to divide by 3). 45 ÷ 27 ≈ 1.67 cubic yards.
- You must order a *whole* number, and 1 yard isn't enough — so round up to 2 cubic yards.
- *Worth keeping:* converting cubic units cubes the factor (1 yd = 3 ft, so 1 yd³ = 27 ft³), and 'order a whole number' problems always round up to cover the need.
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