Acone 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?

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 =

=

Now the slanted height is calculated using Pythagoras theorem:

H =

=

= 10  

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

Arc length of the sector is equal to the perimeter.

Arc length = θ

θ

θ=

(radian)

we know that 1 pi radian = 180 degrees.

So, 1.2 pi radian = degrees

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )