Finding central angle after slicing cone

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?

I drew a diagram. I thought the central angle was 90 degrees because of the 6,8,10 triangle that included the slant height. The answer says 216 degrees. (Thinking)

Re: Finding central angle after slicing cone

Hello, benny92000!

The problem is not stated clearly.

Quote:

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?

The side view of the cone looks like this:

Code:

` B`

*

/:\

/ : \

/ : \

/ : \ 10

/ :8 \

/ : \

/ : \

A *-------*-------* C

: - 6 - : - 6 - :

We see that the slant height is 10 cm.

The circumference of the base is: .

Now we cut the cone and lay it flat.

We have a large sector of a circle of radius 10.

Code:

` B`

* * *

* *

* *

* *

* O *

* * *

* / \ *

10 / \ 10

* / \ *

* / \ *

A * * C

* * *

Length-of-arc Formula: . . where:.

We have: .

Therefore: .

. . . . . . . . . .