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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 \(\pi\)?

 Jan 1, 2019
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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

 

 

cool cool cool

 Jan 1, 2019

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