All six faces of a cube of size 3″ × 3″ ×…
All six faces of a cube of size 3″ × 3″ × 3″ inches are colored and then it is cut into 27 cubes of size 1 inch. How many such small cubes are there in which only two faces are colored?
3″ × 3″ × 3″ इंच आकार के एक घन की सभी छह सतहों को रंगा जाता है। इसके बाद इसे 1 इंच आकार के 27 छोटे घनों में काटा जाता है। ऐसे कितने छोटे घन होंगे जिनकी केवल दो सतहें रंगी हों?
Detailed Solution & Logic
12
Explanation: Small cubes with exactly two colored faces lie on the edges of the cube, excluding the corner cubes.For a cube divided into 3 parts along each edge:Number of such cubes = 12 × (3 − 2) = 12.
व्याख्या : जिन छोटे घनों की केवल दो सतहें रंगी होती हैं, वे घन की किनारों पर होते हैं, लेकिन कोनों पर नहीं।जब प्रत्येक किनारे को 3 भागों में विभाजित किया जाता है:ऐसे छोटे घनों की संख्या = 12 × (3 − 2) = 12.
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