Question

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

Answer 1

The angle against radius, 15cm=30

degree. So the angles are at 1:2:3

from this, we get sides are in the ratio 1:v3:2, The height is 15 v3cm

I=v15v 32+152 = 30

height=15V3&slant height 30 cm

Answer 2

Slant Height is $10\sqrt 3$ cm

Step-by-step explanation:

Given : Cone Radius is 15 cm(r)

$\angle$A which is vertical angle = 60°

• Height is AB

• Radius is BC (15 cm)

• Slant Height is AC

• Hypotenuse is AC in Δ ABC.

$tan \theta = \frac {BC}{AB}$

⇒ tan 60° = $\frac {15}{h}$

⇒ $\sqrt 3 = \frac {15}{h}$

h = $\frac {15}{\sqrt 3} = 5\sqrt 3$ cm

l = $\sqrt {r^2+h^2} = \sqrt {15^2+(5\sqrt 3)^2}$

= $\sqrt {225+75}$

= $\sqrt {300}$

= $10\sqrt 3$ cm

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