devarshi-dt-logo

Question:

The maximum volume (in cu.m) of the right circular cone having slant height 3m is

3√3π

6π

43π

2√3π

Solution:

∴h=3cosθr=3sinθNow,V=1/3πr²h=π/3(9sin²θ)⋅(3cosθ)∴dV/dθ=0⇒sinθ=√2/3Also,d²V/dθ²]sinθ=√2/3=negative ⇒Volume is maximum.When sinθ=√2/3∴Vmax(sinθ=√2/3)=2√3π(in cu.m).