उस गोले का आयतन, जिसकी त्रिज्या 2d/3 है, होगा:

Question

उस गोले का आयतन, जिसकी त्रिज्या 2d/3 है, होगा:

1. A. (32/81)πd³ (Correct answer)
2. B. (23/4)πd³
3. C. (32/3)πd³
4. D. (34/3)πd³

Correct Answer

Option A — (32/81)πd³

Detailed Solution & Explanation

The correct answer is (32/81)πd³.

Key Points

• Volume of a sphere = (4/3)πr³, with r = 2d/3.
• r³ = (2d/3)³ = 8d³/27.
• V = (4/3)π × 8d³/27 = 32πd³/81.

Additional Information

• Related sphere formulae: surface area = 4πr², hemisphere volume = (2/3)πr³, curved surface of hemisphere = 2πr².