What will be thrice of semi vertical angle of the cone whose curved surface area is 2 times the base area.
Answer & explanation
Correct answer: option 4
CSA = πrl
A = πr2
r = radius of the base
l = slant height
CSA = curved surface area
A = Base area
⇒ πrl = 2πr2 (given)
∴ \(\frac{r}{l}\) = \(\frac{1}{2}\)
Semiverticle angle i.e ∠CAD
Let ∠CAD = θ
sin θ = \(\frac{1}{2}\)
θ = 30°
Thrice of semiverticle angle = 3 × 30° = 90°