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A circular sector with a radius of $25$ and a central angle of $345.6^\circ$ is rolled to form a cone. Find the volume of the cone.

 

Please help!

 Feb 27, 2020
 #1
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The  radius  will form  the "slant height" of  the  cone

 

The  arc length  of the sector  will  form the circumference of the  cone

 

This  is    2*pi (25) (345.6  / 360)   =  48pi units

 

The  radius  of  the cone  can be found as

 

Circumference  =  2pi * r

 

48 pi  =  2pi * r     

 

48  = 2r  

 

r  = 24

 

The  height  of  the  cone  =   sqrt [ slant height^2  - radius^2 ]  =

 

sqrt [ 25^2  - 24^2  ]  =

 

sqrt  [625 - 576] = sqrt [49]  = 7

 

Volume (cone)  =  (1/3) pi * r^2 * height  = (1/3)pi ( 24)^2 ( 7)  =  1344 pi  units^3

 

cool cool cool

 Feb 27, 2020

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