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Reserve: limestone dip 30, apparent 20 m

Short answer

True thickness = apparent thickness × cos30° = 20×0.866 = 17.32 m. Reserve = 1128.5 m² × 17.32 m = 19,546 m³ (1.95×10⁴ m³).

Calculate the reserve for limestone bed having dip amount 30°, apparent thickness of 20 m in 1128.5 m² area.

Principle: the apparent (vertical) thickness measured in a borehole is converted to true thickness by t=tvcos⁡δt = t_v\cos\delta; reserve = area ×\times true thickness.

Given

Dip δ=30∘\delta = 30^\circ, apparent thickness tv=20t_v = 20 m, area A=1128.5 m2A = 1128.5\ \text{m}^2.

Calculation

t=20cos⁡30∘=20×0.8660=17.32 mV=1128.5×17.32=19,546 m3\begin{aligned} t &= 20\cos 30^\circ = 20 \times 0.8660 = 17.32\ \text{m} \\ V &= 1128.5 \times 17.32 = 19{,}546\ \text{m}^3 \end{aligned}

Answer: reserve of limestone = 19,546 m³ (about 1.95 × 10⁴ m³).

(If the area is the plan area, the volume is 1128.5×20=22,570 m31128.5 \times 20 = 22{,}570\ \text{m}^3.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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