Question

If half of the vertical angle of a cone of height 3 cm is 60°. Find its volume.

Answer 1

Let ‘B’ be the centre of base of the cone and BC is radius. 

AB is vertical height (i.e.,)

AB = 3 cm 

Given that ∠BAC = 60° 

ΔABC is a right angled triangle, then tan 60° = \(\frac{BC}{AB}\)

⇒ √3 = \(\frac{BC}{3}\) ⇒ BC = 3√3 cm 

Now we have h = 3 cm, r = 3√3 cm 

Volume of the cone = \(\frac{1}{3}\)πr²h 

\(\frac{1}{3}\)π(3√3)² × 3 = 27π cm³ 

(or) 

= \(\frac{594}{7}\) = 84.86 cm³