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

The curved surface area of a right circular cone is 6500π cm², and the diameter of its base is 100 cm. Find the height (in cm) of the cone.

A
125
B
120
C
119
D
115
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 6500π cm², and the diameter of its base is 100 cm. Find the height (in cm) of the cone.
Correct Answer
120
Parameter Extraction: The diameter is provided as 100 cm, logically indicating the base radius (r) equates to precisely 50 cm.Slant Height Derivation: The stand......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Mensuration
Pg. No -
💡 Analysis & Explanation
Parameter Extraction ▼
The diameter is provided as 100 cm, logically indicating the base radius (r) equates to precisely 50 cm.
Slant Height Derivation ▼
The standard formula for Curved Surface Area (CSA) is π * r * l. Inserting the known values gives: 6500π = π * 50 * l. Solving for the slant height (l) equates it to 130 cm.
Pythagorean Implementation ▼
For a cone, height (h), radius (r), and slant height (l) follow the theorem h = √(l² - r²).
Final Calculation ▼
Mapping the digits: h = √(130² - 50²) = √(16900 - 2500) = √14400. The precise root evaluates to 120.
Conclusion ▼
The calculated perpendicular vertical height equals 120 cm.
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