CUET · MATHS · PYQ PAPER 2025
The semi vertical angle of a right circular cone of maximum volume of a given slant height is
- A \(\tan ^{-1} 2\)
- B \(\sin ^{-1}\left(\frac{1}{3}\right)\)
- C \(\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
- D \(\sin ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
Answer & Solution
Correct Answer
(C) \(\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
Step-by-step Solution
Detailed explanation
\(V = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (l\sin\theta)^2 (l\cos\theta) = \frac{1}{3}\pi l^3 \sin^2\theta \cos\theta\) \(\frac{dV}{d\theta} = \frac{1}{3}\pi l^3 (2\sin\theta\cos^2\theta - \sin^3\theta)\)…
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