समान आयतन के तीन घन सिरे से सिरे तक जुड़े हुए हैं। यदि घन का विकर्ण 6√3 सेमी है, तो परिणामी घनाभ का पृष्ठीय क्षेत्रफल ज्ञात कीजिए।

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 4)
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  1. 509 सेमी2
  2. 504 सेमी2
  3. 516 सेमी2
  4. 512 सेमी2

Answer (Detailed Solution Below)

Option 2 : 504 सेमी2
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दिया गया:

घन का विकर्ण = 6√3 सेमी

गणना:

घन का विकर्ण = √3 × भुजा 

⇒ 6√3 = भुजा √3

अत:, भुजा = 6

इसलिए, घनाभ की लंबाई = 3 × 6 = 18 

चौड़ाई = 6 और ऊँचाई = 6

अतः, घनाभ का पृष्ठीय क्षेत्रफल

= 2(lb + bh + lh)

= 2(108 + 36 + 108)

= 2 × 252 सेमी²

= 504 सेमी²

इसलिए, अभीष्ट मान 504 सेमी² है।

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