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NTPC Graduate Tier 1 2025 Shift-3 📅 05 Jun, 2025

A conical vessel has base radius 31 cm and height 45 cm. Water is poured into the vessel until it is full. Find the volume (in cm³) of water in the vessel. (Note: Assuming a typographical error in the official paper where height was intended to be 30 cm to match the given options).

A
9614π
B
9611π
C
9610π
D
9606π
Result Summary
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APEDIA

NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-3
A conical vessel has base radius 31 cm and height 45 cm. Water is poured into the vessel until it is full. Find the volume (in cm³) of water in the vessel. (Note: Assuming a typographical error in the official paper where height was intended to be 30 cm to match the given options).
Correct Answer
9610π
[Volume Formula Setup]: The mathematical formula to calculate the internal volume of a standard cone is V = (1/3) × π × r² × h.[Data Substitution]: Inserti......
💡 Analysis & Explanation
[Volume Formula Setup]
The mathematical formula to calculate the internal volume of a standard cone is V = (1/3) × π × r² × h.
[Data Substitution]
Inserting the given base radius (r = 31 cm). To align with the structurally provided options, we must assume the intended height (h) was 30 cm instead of 45 cm. Thus, V = (1/3) × π × (31)² × 30.
[Arithmetic Resolution]
Squaring the radius gives 31 × 31 = 961. Multiplying this by the simplified height factor (30 / 3 = 10) gives 961 × 10 = 9610.
[Final Output Generation]
Appending the Pi constant, the total volume equates to 9610π cubic centimeters.
Conclusion
The logical volume based on the option matrix is 9610π.