A circular sheet of paper of radius 6 inches is cut into 3 equal sectors, and each sector is formed into a cone with no overlap. What is the height in inches of the cone?

Guest Jun 25, 2018

#1**+2 **

The circumference of the base of each cone will be the arc length of one of the sectors =

2 pi (6) / 3 = 4 pi inches

So....the radius, r, of each cone (in inches) is given by :

4pi = 2 pi * r

4 = 2r

2 = r

And the slant height of each cone is the radius of the original circle

And the radius of the cone and its height will form two legs of a right triangle with a hypotenuse of 6 inches (the slant height)

So...using the Pythagorean Theorem, the cone height, h, is given by :

h = √[ slant height^2 - radius^2 ] = √ [ 6^2 - 2^2 ] = √32 = 4√2 inches

CPhill Jun 25, 2018