একটি ফাঁপা গোলকের বহিঃ ব্যাসার্ধ 4 সেমি এবং অন্তঃ ব্যাসার্ধ 1 সেমি। এই ফাঁপা গোলকের আয়তন কত?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 3)
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  1. 84π সেমি3
  2. 68π সেমি3
  3. 48π সেমি3
  4. 92π সেমি3

Answer (Detailed Solution Below)

Option 1 : 84π সেমি3
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SSC CGL Tier 1 2025 Full Test - 01
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Detailed Solution

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প্রদত্ত:

ফাঁপা গোলকের জন্য,

বহিঃ ব্যাসার্ধ (ro) = 4 সেমি।

অন্তঃ ব্যাসার্ধ (ri) = 1 সেমি।

ব্যবহৃত ধারণা:

ফাঁপা গোলকের আয়তন

ফাঁপা গোলকের আয়তন = 4/3π(ro3 - ri3)

গণনা:

ফাঁপা গোলকের আয়তন = (4/3)π × (43 - 13)

⇒ (4/3)π × (64 - 1)

⇒ (4/3)π × 63

⇒ 84π

∴ ফাঁপা গোলকের আয়তন 84π সেমি3

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