Question

A cone made of cardboard has a vertical height of 8 cm and a radius of 6 cm. If this cone is cut along the slanted height to make a sector, what is the central angle, in degrees, of the sector?

Answer 1

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 = $2\pi r$

$2\pi \times6$ = $12\pi$

Now the slanted height is calculated using Pythagoras theorem:

H = $\sqrt{r^{2}+h^{2}}$

= $\sqrt{6^{2}+8^{2} }$

$\sqrt{36+64}=\sqrt{100}$ = 10  

Let 'θ' is the sector angle that we have to find.  

Arc length of the sector is equal to the perimeter.

Arc length = $10$θ

$12\pi =10$θ

θ=$12\pi /10$

$θ=1.2\pi$ (radian)

we know that 1 pi radian = 180 degrees.

So, 1.2 pi radian = $1.2\times180=216$ degrees