गोले का आयतन 38,808 घन सेमी3 है। गोले का पृष्ठीय क्षेत्रफल कितना है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 4)
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  1. 4455 सेमी2
  2. 4433 सेमी2
  3. 5544 सेमी2
  4. 3344 सेमी2

Answer (Detailed Solution Below)

Option 3 : 5544 सेमी2
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दिया गया है:

गोले का आयतन = 38,808 सेमी³

प्रयुक्त अवधारणा:

गोले के आयतन का सूत्र इस प्रकार है:

V = (4/3)πr³

गोले के पृष्ठीय क्षेत्रफल का सूत्र इस प्रकार है:

A = 4πr²

गणना:

V = (4/3)πr³

38808 = 4/3 × 22/7 × r3

⇒ r 3 = (38808 × 3 × 7)/(4 × 22)

⇒ r3 = (9702 × 3 × 7)/22

⇒ r3 = 441 × 21

⇒ r = 21 सेमी

कुल पृष्ठीय क्षेत्रफल = 4πr2

⇒ 4 × 22/7 × 21 × 21

⇒ 5544 सेमी2

∴ विकल्प 3 सही उत्तर है।

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