Show that the semi vertical angle of a right circular cone …

Maths Differentiation and Applications of Derivatives Maxima and Minima Subjective Type

Published on: August 13, 2026

Show that the semi vertical angle of a right circular cone of maximum volume, of a given slant height is tan − 1 .

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h = λ cos θ

r = λ sin θ

V = π r 2 h

V = π λ 3 sin 2 θ cos θ

= π λ 3 (2sin θ cos 2 θ – sin 3 θ )

= π λ 3 sin θ (2 – 3 sin 2 θ ) = 0 at

sin θ = ⇒ tan θ =

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