एक गोले का आयतन क्या है जिसका पृष्ठीय क्षेत्रफल 124.74 वर्ग सेमी2 है?

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DDA JE Civil Official Paper (Held On: 28 Mar, 2023 Shift 2)
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  1. 133.123 सेमी3
  2. 129.325 सेमी3
  3. 128.324 सेमी3
  4. 130.977 सेमी3

Answer (Detailed Solution Below)

Option 4 : 130.977 सेमी3
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दिया गया है:

पृष्ठीय क्षेत्रफल 124.74 सेमी2 है।

प्रयुक्त सूत्र:

गोले का कुल पृष्ठीय क्षेत्र = 4 π r2

गोले का आयतन = (4/3)π r3

गोले की त्रिज्या = r

गणना:

गोले का कुल पृष्ठीय क्षेत्र = 4 π r2

⇒ 4 π r = 124.74

⇒ r = √(124.74 × 7/88)

⇒ r = 3.15

प्रश्न के अनुसार,

गोले का आयतन = (4/3)π r3 

⇒ (4/3) π × (3.15)3

⇒ 130.977 सेमी3

∴ गोले का आयतन 130.977 सेमी3 है।

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