Questions
If is the angle (semi-vertical) of a cone of maximum volume and given slant height, then is given by
a
2
b
1
c
2
d
3
detailed solution
Correct option is C
Let OB=1,OA=1cosθ and AB=1sinθ(0≤θ≤π/2). Then V=π3(AB)2(OA)=π3l3sin2θcosθ⇒ dVdθ=π3l3sinθ3cos2θ−1 So from dV/dθ=0, we get θ=0 or cosθ=1/3. Also, V(0)=0,V(π/2)=0 and Vcos−113=2πl393 Hence V is maximum when cosθ=1/3, i.e. tanθ=2Talk to our academic expert!
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