Answer:
216 degrees is the answer.
Step-by-step explanation:
The vertical height of the cone = 8 cm
The radius of the cone = 6 cm
The perimeter or circumference of the base of the cone is given by:
P = [tex]2\pi r[/tex]
[tex]2\pi \times6[/tex] = [tex]12\pi[/tex]
Now the slanted height is calculated using Pythagoras theorem:
H = [tex]\sqrt{r^{2}+h^{2}}[/tex]
= [tex]\sqrt{6^{2}+8^{2} }[/tex]
[tex]\sqrt{36+64}=\sqrt{100}[/tex] = 10
Let 'θ' is the sector angle that we have to find.
Arc length of the sector is equal to the perimeter.
Arc length = [tex]10[/tex]θ
[tex]12\pi =10[/tex]θ
θ=[tex]12\pi /10[/tex]
[tex]θ=1.2\pi[/tex] (radian)
we know that 1 pi radian = 180 degrees.
So, 1.2 pi radian = [tex]1.2\times180=216[/tex] degrees
