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A circle has a radius of 25. A circular sector, with an angle of 320 degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.

 Jul 6, 2021
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The  radius  of  25  will be  the slant height of the  cone

The  circumference of the  cone's  base =   2pi  (25)   *  32 / 36  =  400pi  /  9

The radius  of  the cone  =    (400pi / 9)  / (2pi)   =  400/18 =  200/9

Using  the Pythagorean Theoren, the height of  the  cone =   sqrt  ( 25^2  -  (200/9)^2  )   =  (25./9)sqrt 17

 

Volume of cone   =  (1/3)pi  *[ 200/9]^2 *  [ (25/9)sqrt 17 ]  ≈  5922.8 units^3

 

cool cool cool

 Jul 6, 2021

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