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)

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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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, (= 3.14)

Surface Areas and Volumes

Mathematics

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)