Conics

(b) tan^-1 2.

Volume of a cone = πR²h/3

V = π(S²- h²)h/3         ................S - Slant height, R - Radius, h - height, V - Volume.

dV/dh = 0            .............Note that given slant height, S, so it's a constant.

π(S² - 3h²)/3 = 0

S² = 3h²

R² = S² - h²

= 2h²

semi vertical angle of a cone α, tan α = R/h = 2

α = tan^-1 (2)

Regards,

Team,

TopperLearning.