Application of DerivativeHard

Question

In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is l. The altitude of the prism for which the volume is greatest, is :

Options

A.l/2
B.l/√3
C.l/3
D.l/4

Solution

     
l2 = h2 + x2
Area of base (triangle) is a2
3x = a
Volume V = h a2
= h . 4 . 3.x2
= 3 √3 h (l2 - h2)
= 3 √3 (l2 - 3h2)
V is maximum when h =

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