A cone is formed from a 300-degree sector of a circle of radius 18 by aligning the two straight sides. What is the result when the volume of the cone is divided by \(\pi\)?

Guest Jan 1, 2019

#1**+1 **

We can find the radius of the cone thusly :

Perimeter of cone = Perimeter of sector shown

2 pi * ( radius of cone) = (300 / 360) 2 pi * 18

radius of cone = (5/6) * 18

radius of cone = 15

The height of the cone is √ [ 18^2 - 15^2 ] = √99 = 3√11

So....the volume of the cone is

(1/3) pi * (radius)^2 * height =

(1/3) pi ( 15)^2 * 3√11 =

pi * 225√11

Dividing this by pi gives

225√11

CPhill Jan 1, 2019