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NTPC Graduate Tier 1 2025 Shift-2 📅 05 Jun, 2025

The curved surface area of a right circular cone is 5400π cm², and the diameter of its base is 144 cm. Find the height (in cm) of the cone.

A
16
B
21
C
22
D
20
Result Summary
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NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-2
The curved surface area of a right circular cone is 5400π cm², and the diameter of its base is 144 cm. Find the height (in cm) of the cone.
Correct Answer
21
Radius Derivation: The problem establishes the full base diameter as 144 cm, which inherently splits to give a base radius (r) of 72 cm.Slant Height Execution: ......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Mensuration
Pg. No -
💡 Analysis & Explanation
Radius Derivation ▼
The problem establishes the full base diameter as 144 cm, which inherently splits to give a base radius (r) of 72 cm.
Slant Height Execution ▼
The geometric formula for the Curved Surface Area (CSA) of a cone is πrl. Equating the values: 5400π = π * 72 * l. Solving for the slant height (l) yields 5400 / 72 = 75 cm.
Height Resolution via Pythagoras ▼
The cone's dimensions form a right triangle dictating the relation h = √(l² - r²).
Final Computation ▼
Plugging in the vectors: h = √(75² - 72²). Utilizing the algebraic identity a² - b² = (a - b)(a + b) simplifies this to √(3 * 147) = √441. The exact square root is 21.
Conclusion ▼
The direct vertical height evaluates perfectly to 21 cm.
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