Correct Answer - Option 1 : 12 cm
Given:
Curved surface area = 0.407 m2
Radius of the base = 35 cm
Formula used:
Curved surface area (C.S.A) = πrl
\({\rm{h}}={\rm{\;}}\sqrt {{{\rm{l}}^{2{\rm{\;}}}} - {\rm{\;}}{{\rm{r}}^2}} \)
Where r = radius, l = slant height, h = height
Calculation:
According to the question.
πrl = 0.407 m2
⇒ 22/7 × 35 × l = 4070 (1m2 = 10000 cm)
⇒ 22 × 5 × l = 4070
⇒ 110l = 4070
⇒ l = 37
⇒ l = 37 cm
⇒ \({\rm{h}} = {\rm{\;}}\sqrt {{{\rm{(37)}}^{2{\rm{\;}}}} - {\rm{\;}}{{\rm{(35)}}^2}} \)
⇒ \({\rm{h}} = {\rm{\;}}\sqrt {{{\rm{1369}}^{{\rm{\;}}}} - {\rm{\;}}{{\rm{1225}}}} \)
⇒ \({\rm{h}} = {\rm{\;}}\sqrt {144{{\rm{}}}}\)
⇒ h = 12
⇒ h = 12 cm
∴ Height of the cone is 12 cm