एक घनाभ का आयतन, एक घन के आयतन का दोगुना है। यदि घनाभ के आयाम (8 m × 8 m × 16 m) हैं, तो घन का कुल पृष्ठीय क्षेत्रफल कितना होगा?

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SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 1)
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  1. 316 m2
  2. 288 m2
  3. 324 m2
  4. 384 m2

Answer (Detailed Solution Below)

Option 4 : 384 m2
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दिया गया है:

एक घनाभ का आयतन, एक घन के आयतन का दोगुना है।

ऊँचाई  = 16 m 

चौड़ाई = 8 m 

लंबाई = 8 m 

प्रयुक्त सूत्र:

घनाभ का आयतन = लंबाई × चौड़ाई × ऊँचाई

घन का आयतन = (भुजा) 3

गणना:

घनाभ का आयतन = 8 × 8 × 16 

= 1024

घनाभ का आयतन = 2 × घन का आयतन

घनाभ का आयतन = 2 × (भुजा) 3

(भुजा)3 = 1024/2 = 512 m 

भुजा = 8 m

घन का कुल पृष्ठीय क्षेत्रफल = 6 × 64

= 384 m 2

घन का कुल पृष्ठीय क्षेत्रफल 384 m 2 है।
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