Question

If half of the vertical angle of a cone height 3cm is 60 degrees find its volume

Answer 1

Solution:

      →→ Half of vertical angle of cone of height 3 cm , Called ,Semi Vertical Angle= 60°

Height (H)= 3 cm

And, OB= Radius =r cm

In  Right ΔO AB

$tan 60=\frac{AB}{OA}\\\\ \sqrt3=\frac{r}{H}\\\\ r=3 \times \sqrt3$

→→ Volume of cone =

                         $=\frac{1}{3}\times \pi \times r^2 \times H\\\\ =\frac{1}{3}\times (3.14) \times (3\sqrt{3})^2\times 3\\\\ = 3.14  \times 27\\\\= 84.78$Centimeter cube

Answer 2

Given :

Half of the vertical angle of a cone height 3cm is 60 degrees

To Find :

Find its volume

Solution:

Identity : $Tan\theta = \frac{Perpendicular}{Base}$

Height of cone = 3 cm

Half of the vertical angle of a cone height 3cm is 60 degrees

$Tan 60^{\circ}=\frac{Radius}{Height}=\frac{Radius}{3}\\\sqrt{3}=\frac{Radius}{3}\\3 \sqrt{3}=Radius$

Volume of cone =$\frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times (3\sqrt{3})^2 \times 3=84.857 cm^3$

Hence The volume of cone is 84.857 cubic cm