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# An equilateral triangle of side 12 centimeters is rotated about an altitude to form a cone. What is the number of cubic centimeters in the v

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An equilateral triangle of side 12 centimeters is rotated about an altitude to form a cone. What is the number of cubic centimeters in the volume of the cone?
michaelcai  Oct 24, 2017

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The height of the cone will be the same as the height of the triangle.

height  =  12 sin 60°  =  12 √3 / 2   =  6√3

The radius of the cone will be half of the base of the triangle.

radius  =  12 / 2  =  6

So..   volume of cone  =  (1/3)(pi)(6)2(6√3)   =   (1/3)(pi)(36)(6√3)  =  72 pi √3  cubic centimeters

hectictar  Oct 24, 2017
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#1
+5261
+1

The height of the cone will be the same as the height of the triangle.

height  =  12 sin 60°  =  12 √3 / 2   =  6√3

The radius of the cone will be half of the base of the triangle.

radius  =  12 / 2  =  6

So..   volume of cone  =  (1/3)(pi)(6)2(6√3)   =   (1/3)(pi)(36)(6√3)  =  72 pi √3  cubic centimeters

hectictar  Oct 24, 2017

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