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The maximum volume (in cu.m) of the righ...

The maximum volume (in cu.m) of the right circular cone having slant height 3m is `ksqrt(3)pi` . The value of k is ________.

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The correct Answer is:
2
`R^(2)+H^(2)=9impliesR^(2)=9-H^(2)`
volume `=1/3pi H(9-H^(2))`
`(H^(2)+(9-H^(2))/2+(9-H^(2))/2)/3 geroot(3)(H^(2)((9-H^(2))/2)^(2))`
i.e. `[H(9-H^(2))]^(2//3)le3xx4^(1//3)`
Hence volume `le1/3xxpixx3sqrt(3)xx2le2pisqrt(3)`
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