If 537 km² were the plan area, what would the volume be?

Area x true thickness = 143.7 km³

Reserve: quartzite 400 m, 537 km2

Short answer

True thickness = 400 cos48° = 267.65 m = 0.2677 km. Reserve = area × true thickness = 537 km² × 0.2677 km = 143.7 km³ (1.44×10¹¹ m³).

Calculate the reserve for construction of quartzite bed having vertical thickness 400 m at S72°W/48°SE in an area of 537 km².

Principle: reserve = area $\times$ true thickness, with $t = t_v\cos\delta$ .

$t_v = 400$ m, attitude S72°W/48° SE (dip $\delta = 48^\circ$ ), area $A = 537\ \text{km}^2$ .

\begin{aligned} t &= 400\cos 48^\circ = 400 \times 0.6691 = 267.65\ \text{m} = 0.2677\ \text{km} \\ V &= 537 \times 0.2677 = 143.73\ \text{km}^3 = 1.44 \times 10^{11}\ \text{m}^3 \end{aligned}

Answer: reserve of quartzite = 143.7 km³ (1.44 × 10¹¹ m³).

(If 537 km² is the plan area, the volume under it is $537 \times 0.4 = 214.8\ \text{km}^3$ .)

✓ Answer checked by Claude Opus 5.5 (high effort)