GATE 2025 AR — Architecture – Question 48
The projected sky diagram shows hatched sky and black obstructions within a circle of radius 3. Quarter-sector sky radii are 2, 1, 1 and 3 units as shown. Find sky-view factor to two decimals.
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Correct answer: 0.40 to 0.43
Explanation
Projected visible area is the sum of four quarter-discs:π(2²+1²+1²+3²)/4=15π/4. Full projected hemisphere circle isπ×3²=9π. The area ratio is(15π/4)/(9π)=15/36=0.416667, or 0.42. Hatched regions represent visible sky; black regions are excluded.
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