Question

a piece of paper in the shape of sector of circle is rolled up to form a right circular cone. what is the measure of the angle theta if its height is twelve centimeter and radius is 5 cms

Answer 1

As always, draw a picture.

The radius of the circle is the slant height of the cone.

The arc length of the paper is the circumference of the cone.

So, the cone's slant height is 13
The circumference of the cone is 10π

So, the angle θ of the sector is found using

s = rθ
10π = 13θ