Thread: 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.

Hello, benny92000!

The problem is not stated clearly.

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: .

. . . . . . . . . .