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Probability

Question
CBSEENMA9003676

If h, c, v are respectively the height, curved surface and the volume of a cone, prove that 3πvh3 – c2h2 + 9v2 = 0

Solution

Let the base radius and the height of the cone be r and h respectively.
Let the slant height of the cone be l.
Then,

c = straight pirl 
            equals πr square root of straight r squared plus straight h squared end root
straight v equals 1 third πr squared straight h
therefore space space space space 3 πvh cubed minus straight c squared straight h squared plus 9 straight v squared
space space space space space space space equals 3 straight pi open parentheses 1 third πr squared straight h close parentheses straight h cubed minus straight pi squared straight r squared left parenthesis straight r squared plus straight h squared right parenthesis straight h squared space plus space 9 open parentheses 1 third πr squared straight h close parentheses squared
space space space space space space space space space space space space space space space

= π2r2h2 – π2r4h2 – π2r4 + π2r4h4 = 0

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