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True thickness: limestone vertical 600 m

Short answer

True thickness = vertical thickness × cos(dip) = 600 cos50° = 385.7 m.

Calculate the true thickness of limestone bed having vertical thickness 600 m at North 75°E/50° NW in an area of 550 km².

Principle: the vertical thickness tvt_v (as in a vertical hole) is converted to the true thickness (perpendicular to bedding) by

t=tvcos⁡δt = t_v\cos\delta

where δ\delta is the dip of the bed. The strike (N75°E) and dip direction (NW) do not affect the thickness; only the dip amount, 50∘50^\circ, is needed.

Calculation

t=600cos⁡50∘=600×0.6428=385.67 m\begin{aligned} t &= 600\cos 50^\circ \\ &= 600 \times 0.6428 \\ &= 385.67\ \text{m} \end{aligned}

Answer: true thickness of the limestone = 385.7 m.

Volume under 550 km² (for reserve)

V=550 km2×0.38567 km=212.1 km3≈2.12×1011 m3V = 550\ \text{km}^2 \times 0.38567\ \text{km} = 212.1\ \text{km}^3 \approx 2.12\times 10^{11}\ \text{m}^3

(taking the 550 km² as the area measured on the bed).

✓ Answer checked by Claude Opus 5.5 (high effort)

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