ACT (Enhanced)MathematicsMedium
A civil engineer is designing a pedestrian bridge. The maximum allowable stress (S) on a support beam is inversely proportional to its cross-sectional area (A). If a beam with a cross-sectional area of 0.5 m² can withstand a stress of 200 kPa, what stress can a beam with a cross-sectional area of 0.8 m² withstand?
- A100 kPa
- B160 kPa
- C320 kPa
- D125 kPa
Show answer & explanationAnswer & explanation
Correct answer: D. 125 kPa
Since stress (S) is inversely proportional to area (A), S = k/A, where k is the constant of proportionality. Using the given values, k = S * A = 200 kPa * 0.5 m² = 100 kPa·m². For the new area, S = 100 kPa·m² / 0.8 m² = 125 kPa.
Why the other options are wrong
- A. This would be the result if the stress was directly proportional and area increased by a factor of 2.
- B. This is a plausible distractor if the inverse relationship was misapplied or a calculation error occurred.
- C. This would be the result if stress was directly proportional to area.
Inverse Proportionality
Two quantities are inversely proportional if their product is constant; as one quantity increases, the other decreases proportionally.
- Expressed as y = k/x or xy = k, where k is the constant of proportionality.
- Graphs as a hyperbola.
- Common in physics (e.g., Boyle's Law, Ohm's Law).
Memory trick: Direct is multiply, Inverse is divide to find the constant.