Question

Slant height of a cone is 8cm and half of its vertical angle is 60° as shown in
the figure. Find the radius of the base of the cone.
om
SI​

Answer 1

The radius of the cone is  16.√3 / 3  cm

Step-by-step explanation:

We are given:

• The height of cone = 8 cm
• Vertical angle = 60°

To find:

Diameter "d" = ?

Semi vertical angle "x" = 60°/2 = 30°

8 =  √3 / 2 x AC

8 x 2 = √3 x Ac

16 = √3 x AC

AC = 16 /√3

AC = 16√3 / 3

Segment O.C = 1/2 x AC

O.C = 1/2 x 16√3 / 3 = 8√3 / 3

Radius "r"  = 8√3 / 3

Diameter = 2×r = 2 x 8√3 / 3 = 16 x √3 / 3

Diameter = 16 x 1.73 / 3 = 27.68 / 3 = 9.2 cm

Hence the radius of the cone is  16.√3 / 3  cm

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