GATE 2024 MN – Question 59
The shaded longitudinal section shows recovered ore in a repeating stope layout. Thickness is uniform. The dimensions shown are 60 m between levels, 4 m rib pillars, 3 m sills, 6.25 m corner radii and 2.5 m access openings. Find ore recovery as a percentage, rounded to two decimals.
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Correct answer: 68.00 to 71.00
Explanation
The full-width stope opening is 2R+2.5 = 15 m. Between the dashed rib centre lines, one repeating unit contains this opening plus one complete 4 m rib, so gross area is 60×19 = 1140 m². Between the two 3 m sills, the opening starts as a 54×15 rectangle. Four rounded corners remove (4−π)R²; the two 2.5×3 m access openings through the sills add 15 m². Recovered area is 810−(4−π)×6.25²+15 = 791.47 m². Recovery is 791.47/1140×100 = 69.43%. Counting two complete boundary ribs would double-count the shared pillars.