Multiple choice

In a right circular cone the radius of its base is 6 cm and its height is 14 cm. A cross section is made through the mid-point of the height parallel to the base. The volume of the lower position is? एक गोलाकार शंकु में इसके आधार की त्रिज्या 6 सेमी है और इसकी ऊँचाई 14 सेमी है। एक क्रॉस सेक्शन को आधार के समानांतर ऊंचाई के मध्य-बिंदु के माध्यम से बनाया गया है। निम्न स्थिति का आयतन है?

  1. 528

  2. 366

  3. 498

  4. 462

  5. None of these इनमे से कोई नही
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The full cone volume is (1/3)πr²h = (1/3)π(6)²(14) = 168π cm³. When cut at the midpoint of height (7cm), the radius at that level is 3cm by similarity. The upper small cone has volume (1/3)π(3)²(7) = 21π cm³. Therefore, the lower frustum volume = 168π - 21π = 147π ≈ 462 cm³. The key is recognizing the smaller cone removed from the top.

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