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An equilateral triangle of side 14 centimeters is revolved about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone? Express your answer to the nearest whole number, without units.

 Dec 12, 2019
 #1
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The radius of the cone is 14/sqrt(3), and the height of the cone is 28, so the volume of the cone is 1/3*pi*(14/sqrt(3))^2*28 = 5488*pi/9.  To the nearest whole number, this is 1916.

 Dec 12, 2019
 #2
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The altitude  of the  cone  =   7sqrt(3)   cm

 

The radius  of the  cone =  7  cm

 

The volume of the  cone  =

 

pi  ( 7)^2  ( 7sqrt(3) ) / 3    =   7^3 pi  / sqrt (3)   ≈    622  cm^3

 

 

cool cool cool

 Dec 13, 2019

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