Q11 of 79 Page 229

If the vertical angle and the radius of a right circular cone are 60° and 15 cm respectively, then find its height and slant height.

Given : Radius of cone = r = 15 cm

Vertical angle = θ = 60°


To find : height of cone = h = ?


Slant height of cone = l = ?


Formula : l =


Solution :


RAT.png


Here, the vertical angle = ∠ A = 60°


AB = height


BC = radius = 15 cm


AC = slant height


In Δ ABC, AC is the hypotenuse.


tan θ =


⇒ tan 60° =


=


∴ h = = 5√3 cm


l = = = l = = 10√3 cm


∴ The height and slant height of the right circular cone are 5√3 cm and 10√3 cm respectively.


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