Q15 of 79 Page 229

Radius and slant height of a solid right circular cone are in the ratio 3 : 5. If the curved surface area is 60 πsq.cm, then find its total surface area.

Given : Ratio of radius and slant height of cone = r : l = 3 : 5

CSA of cone = 60 sq.cm


To find : TSA of cone = ?


Formula : CSA of cone = rl


TSA of cone = r (r + l)


Solution : Ratio of radius and slant height = 3 : 5


⇒


r =


CSA of cone = rl


60 = × × l


⇒ l2 = = 100


⇒ l = 10 cm


∴ r = = = 6 cm


TSA of cone = r (r + l) = × 6 (6 + 10) = = = cm2


∴ The total surface area of the solid right circular cone is cm2.


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