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January 31, 2015

January 31, 2015

Posted by **mathemagiacian** on Friday, August 9, 2013 at 11:59am.

I just want the answer. Thanks! :)

- ADVANCED AMC8 GEOMETRY QUESTION/MATH -
**Jai**, Saturday, August 10, 2013 at 2:02amNote that an equilateral triangle is a triangle where all lengths of the sides are equal.

If you revolve the triangle about its altitude (or the height), you'll generate a cone (just try to imagine or draw the figure). Therefore, the height of the cone is equal to the height of triangle, and its radius is equal to half of one side of the equilateral triangle, which is 14/2 = 7 cm (radius).

To get the height, use pythagorean theorem:

c^2 = a^2 + b^2

where

c = hypotenuse (in this case, 14 cm)

a = height of triangle (which is also cone height)

b = base (which is also the cone radius)

Substituting,

14^2 = a^2 + 7^2

a^2 = 14^2 - 7^2

a^2 = 147

a = 7*sqrt(3)

Finally, we get the volume of cone. Recall that the volume of cone is just

V = (1/3)*(pi)*(r^2)*h

Substituting,

V = (1/3)(3.14)(7^2)(7*sqrt(3))

Now solve for V. Units in cubic centimeters.

Hope this helps~ :)

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