SOLUTION: 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 pris

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.
RELATED QUESTIONS
Hi, I am having some trouble with a Geometry question for an investigation, which... (answered by stanbon,xinxin)

The larger circle circumscribes an equilateral triangle, which circumscribes a small... (answered by Theo)

Hi, I am having trouble with a problem on my homework, I hope some one can help me,The... (answered by frostusna,checkley75)

A right prism with equilateral triangular bases whose sides are 6 in. and the height of... (answered by Nate)

Hi! How are you all Today? So I am having a bit of trouble with this question. The... (answered by jim_thompson5910,checkley71)

I am having a problem with this word problem, I am not good at them and need some help. (answered by scott8148)

Hi, I am currently working on creating my own geometry word problems using the Desmos... (answered by math_tutor2020)

I am not having that much difficulty with Geometry, basically I am new to it. I tend to... (answered by solver91311)

Hi, I have this problem to solve, and would really appreciate some help: |5-2x|>3 I... (answered by tutorcecilia)