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

216 degrees is the answer.

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 *6` =
`12\pi`

Now the slanted height is calculated using Pythagoras theorem:

H =
`\sqrt{r^(2)+h^(2)}`

=
`\sqrt{6^(2)+8^(2) }`

`√(36+64)=√(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*180=216` degrees