A valley in the Himalayas is 100 km long, 10 km wide on average, and has an average depth of 200 m. Calculate the approximate volume of this valley in cubic metres.
Answer
2×10^11 m³
The correct answer is 2×10^11 m³ — So the valley’s volume is about 2×10¹¹ cubic metres.
Step-by-step solution
- Compute the horizontal area: 100 km × 10 km = 1,000 km².
- Convert the area to square metres: 1,000 km² = 1,000 × (1,000 m)² = 1,000 × 1,000,000 m² = 1.0 × 10⁹ m².
- Multiply the area by the average depth to get volume: 1.0 × 10⁹ m² × 200 m = 2.0 × 10¹¹ m³.
- So the valley’s volume is about 2×10¹¹ cubic metres.
Common mistake: Using km² directly with metres, leading to units error
Concept tested: Valley volume calculation
Published · How this solution was prepared and checked
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