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The right circular cone of largest volume that can be enclosed by a sphere of 1 m radius has a height of 
  • a)
    1/3 m
  • b)
    2/3 m 
  • c)
  • d)
    4/3 m 
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The right circular cone of largest volume that can be enclosed by a sp...
The correct option is c) 4/3 m
Let height (AM) of the cone is h meters.

OA=OB=1m
Therefore,
Radius of base of right circular cone is
r = BM = (OB2-OM2)1/2
r = (1-(h-1)2)1/2
r = (2h-h2)1/2
Volume of the cone V=1/3πr2h = 1/3π(2h - h2)h
For maximum volume V
dV/dH =O ⇒ π/3(4h-3h2) = 0
⇒ h = 0
or
h= 4/3
But h = 0 (Not possible)
So, required height, h = 4/3 m
 
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The right circular cone of largest volume that can be enclosed by a sphere of 1 m radius has a height ofa)1/3 mb)2/3 mc)d)4/3 mCorrect answer is option 'C'. Can you explain this answer?
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