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The curved surface area of a right circular cone is 0.407 m2 and its radius of the base is 35 cm. Find height of the cone.
1. 12 cm
2. 13 cm
3. 6 cm
4. 24 cm

1 Answer

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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

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