GATE 2023 AR — Architecture – Question 48
The figure is the surface development of a closed three-dimensional object; dotted lines are folds and dimensions are centimetres. Find its volume in cm³, rounded to one decimal place.
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Correct answer: 25.5 to 25.5
Explanation
Folding forms a 3 cm-long prism with a 3 cm×3 cm cross-section whose upper corner is cut by a 1 cm×1 cm right triangle. Cross-sectional area is 9−(1×1)/2=8.5 cm². Multiply by the 3 cm prism length to obtain 25.5 cm³. Fold lines separate faces; adding face areas would give surface area rather than volume.