36 मीटर लम्बाई, 18 मीटर चौड़ाई और 9 मीटर ऊँचाई वाले एक घनाभ को पिघलाकर एक घन बनाया जाता है। घन के विकर्ण की लम्बाई ज्ञात कीजिए।

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SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 3)
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  1. 18 √3 मीटर
  2. 15 √3 मीटर
  3. 12 √3 मीटर
  4. 17 √3 मीटर

Answer (Detailed Solution Below)

Option 1 : 18 √3 मीटर
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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दिया गया है:

36 मीटर लम्बाई, 18 मीटर चौड़ाई और 9 मीटर ऊँचाई वाले एक घनाभ को पिघलाकर एक घन बनाया जाता है।

प्रयुक्त सूत्र:

घनाभ का आयतन = L × H × B

घन का आयतन = a3

यहाँ,

L = लम्बाई

B = चौड़ाई

H = ऊँचाई

a = घन की भुजा

गणना:

मान लीजिए कि निर्मित घन की भुजा a है। 

प्रश्न के अनुसार,

घनाभ का आयतन = घन का आयतन

इसलिए,

36 × 18 × 9 = a3 

5832 = a3 

⇒ a3 = 183

⇒ a = 18

इसलिए, घन का विकर्ण 18√3 है।

∴ घन के विकर्ण की लम्बाई 18√3 है।

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