How to Find Height of Cone from Sector it was made with - Circular Sector and Right Cone

Exam question involving a circular sector and a right cone, we learn how to find the height of the cone using nothing but the circular sector it was made from. The idea is to use the following two facts: The slant height (or sloping edge) of the cone is equal to sector’s radius The circumference (or perimeter) of the cone’s circular base is equal to the sector’s arc length Using these two fact we can rearrange the equation for the cone’s slant height to make the height, h, the subject. This question is used for both my IGCSE and IB Mathematics classes. ******* Exercise ******* The circle, with centre O, has radius 10cm. Angle AOB = 50°. The minor sector AOB is removed. The major sector is formed into a cone by joining OA to OB. Calculate the height of the cone. ******* TIMESTAMPS ******* 00:00 Introduction 00:29 The Exercise (Exam Question) 01:30 Beginning of Solution 02:38 Formula involving the cone's height: volume and slant height (sloping edge) 04:26 Choosing the right formula, slant height = radius of sector 05:23 Slant height (sloping edge) where formula comes from 07:44 Back to Exercise 08:02 Radius at Base of Cone = Arc Length of Sector 10:06 Calculating Radius at the base of the cone 11:33 Calculating the Height of the Cone 14:28 Conclusion