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Question

If a right circular cone having maximum volume is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is :

A
62π
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B
63π
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C
82π
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D
83π
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Solution

The correct option is D 83π

From the figure,
r2+(h3)2=32r2+h26h=0r2=6hh2
Volume of the cone
V=13πr2h =π3h(6hh2)=π3(6h2h3)
Finding the maximum volume,
dVdh=0(12h3h2)=0h=0 or h=4
So, h=4r=6hh2=22
The curved surface area
=πrl=πrr2+h2=π×22×8+16=83π

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