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Question 1136029: Hi!
I am having some trouble with this geometry problem:
A prism, bases of which are equilateral triangles, circumscribes a sphere of radius 6. What is the volume of the prism?
I know that the height of the prism is 12, because the radius of the circle is 6, so you double it to get the diameter and the height of the prism.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
A horizontal cross section (a view from the top of the prism) will be a circle inscribed in an equilateral triangle.
Whenever you are working a problem with equilateral triangles inscribed in circles, or circles inscribed in equilateral triangles, draw the lines in the triangle that divide the equilateral triangle into 6 30-60-90 right triangles.
If you do that in your problem, you can use the given radius of the circle and your knowledge about the side lengths of 30-60-90 right triangles to find the area of the equilateral triangular base of the prism.
Then the volume is that base, times the height of 12 that you already know.
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