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A circle has a radius of 25. A circular sector, with an angle of \(90\) degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.

 Feb 10, 2022
 #1
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The slant height of the cone = the radius of the circle

 

The  circumference  of  the of the  whole circle =   2pi * 25  =  50 pi

 

Since  90 degrees is taken out - (1/4) of the circumference- then the circumference of the  cone = (50)pi  * (3/4) =   37.5 pi

 

The radius of the cone  = 1/2 of this =     ( 37.5 pi) / (2pi)  =  18.75 

 

The height of the cone =   sqrt ( slant height ^2 - radius^2 )  =  sqrt ( 25^2 - 18.75^2)   ≈ 16.54

 

The volume is   (1/3) * pi * ( 18.75)^2 * ( 16.54) ≈  6089.3  ( cubic units)

 

cool cool cool

 Feb 10, 2022
 #2
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Read the question again!!!

 

90º sector is rolled into a cone!!!

Guest Feb 10, 2022

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