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Sponsor Area

Probability

Question
CBSEENMA9003678
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The radius and height of a right circular cone are in the ratio of 5 : 12. If its volume is 314 cm3, find the slant height and radius of the cone, (straight pi= 3.14) 

Solution

Let the radius and height of the cone be 5k and 12k respectively. Then,
r = 5k
h = 12k
      space space space space space space space space space straight V equals 1 third πt squared straight h equals 314 rightwards double arrow space space space 1 third cross times 3.14 cross times left parenthesis 5 straight k right parenthesis squared cross times left parenthesis 12 straight k right parenthesis equals 314 rightwards double arrow space space space space straight k equals 1 therefore space space space space space straight r equals 5 space cm space space space space space space space space straight h space equals space 12 space cm therefore space space space space space l space equals square root of straight r squared plus straight h squared end root space space space space space space space space space space equals square root of 5 squared plus 12 squared end root space space space space space space space space space space space equals space 13 space cm
Hence, the slant height and radius of the cone are 13 cm and 5 cm respectively.

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