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Q.
The lateral edge of a regular hexagonal pyramid is $1 cm$. If the volume is maximum, then its height must be equal to :
Application of Derivatives
Solution:
$x ^2+ h ^2=1 ; V =\frac{1}{3} \cdot 6 \cdot \frac{\sqrt{3}}{4} x ^2 h =\frac{\sqrt{3}}{2} h \left(1- h ^2\right)$
$V ^{\prime}( h )=0 \Rightarrow h =\frac{1}{\sqrt{3}} \Rightarrow V _{\max }=1 / 3$
