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Aggregate reserve: sandstone N44W/36, 82 m

Short answer

True thickness = vertical thickness × cos(dip) = 82 cos36° = 66.34 m. Area along bed = 2700 m × 620 m = 1.674×10⁶ m². Reserve = area × true thickness = 1.11×10⁸ m³.

The attitude of sandstone bedrock is N44°W/36°. The difference of top and bottom of bedrock is 82 m. Calculate the reserve of aggregate in 2.7 km strike length and 0.62 km dip length of rock quarry site.

Principle: reserve = area on the bed ×\times true thickness, with t=tvcos⁡δt = t_v\cos\delta.

Given

Attitude N44°W/36° (dip 36∘36^\circ), vertical thickness tv=82t_v = 82 m, strike length 2.7 km, dip length 0.62 km (along the dip of the bed).

Calculation

t=82cos⁡36∘=66.34 mA=2700×620=1.674×106 m2V=1.674×106×66.34=1.11×108 m3\begin{aligned} t &= 82\cos 36^\circ = 66.34\ \text{m} \\ A &= 2700 \times 620 = 1.674 \times 10^6\ \text{m}^2 \\ V &= 1.674 \times 10^6 \times 66.34 = 1.11 \times 10^8\ \text{m}^3 \end{aligned}

Answer: reserve of aggregate = 1.11 × 10⁸ m³ (about 111 million m³ = 0.111 km³).

✓ Answer checked by Claude Opus 5.5 (high effort)

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