UPSC CAPF (AC) 2026 Paper I · Question 58

Question 58 of the UPSC CAPF (AC) 2026 Paper I (19 July 2026). Try it first, then open the answer and explanation.

1. CAPF 2026 · P-I · Q58 · General Mental Ability · Arithmetic

   A metallic cylindrical disc of radius 7 cm is melted and 22 square-shaped solids of the same thickness are made. If l cm is the side length of these squares, then (in cm)

   1. 2.5 < l < 2.6
   2. 2.6 < l < 2.7
   3. 2.7 < l < 2.8
   4. 2.8 < l < 2.9

   7 cm त्रिज्या वाली एक धात्विक बेलनाकार चक्रिका (cylindrical disc) को पिघलाया जाता है और समान मोटाई के 22 वर्गाकार ठोस (solids) बनाए जाते हैं। यदि इन वर्गों की भुजा की लंबाई l cm है, तो (cm में)

   1. 2.5 < l < 2.6
   2. 2.6 < l < 2.7
   3. 2.7 < l < 2.8
   4. 2.8 < l < 2.9
   Show answer

   Answer: (2) 2.6 < l < 2.7

   उत्तर: (2) 2.6 < l < 2.7

   With the same thickness t, volume is conserved: (22/7) × 7² × t = 22 × l² × t, so 154 = 22l² and l² = 7. Hence l = √7 ≈ 2.646 cm, which lies between 2.6 and 2.7.

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