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If the ratio of the circumference of the base of a right circular cone of radius r to its height is 3 : 1, then what is the area of the curved surface of the cone?
  • a)
    3πr2
  • b)
    [2πr2 √(4π2 + 9)]/3
  • c)
    [πr2 √(π2 + 1)]/3
  • d)
    [πr√(4π2 + 9)]/3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If the ratio of the circumference of the base of a right circular cone...
Given 2πr/h = 3/1
∴ r : h = 3 : 2π
l = √(r2 + h2)
⇒ r × √[1 + (h/r)2]
⇒ r × √[1 + (2π/3)2] = r/3 × √(4π2 + 9)
Curved surface area of cone = πrl
⇒ πr × r/3 × √(4π2 + 9)
⇒ [πr2 √(4π2 + 9)]/3
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