Question

find the diameter of the circular base of right circular cone whose slant height is 8 cm and semi vertex angle is 60 degree​

Answer 1

The diameter of the circular base is $8\sqrt{3}$ cm.

Step-by-step explanation:

*Refer the figure attached.

we are given the slant height = 8 cm

so, 8 = $\sqrt{h^2+r^2}$

64 = $h^2+r^2$     ......(1)

We can understand that:

$cos60\degree = \dfrac{h}{8}$

$\dfrac{1}{2} = \dfrac{h}{8}$

h= 4 cm

Also,

$tan60\degree = \dfrac{r}{4}$

$\sqrt{3} = \dfrac{r}{4}$

$r = 4\sqrt{3}$

Therefore, the diameter = $2r = 8\sqrt{3}$

Thus, the diameter of the circular base is $8\sqrt{3}$ cm.

Answer 2

Answer:

Step-by-step explanation: