SOLUTION: A right, regular triangular prism has a circular cylinder inscribed in it (see figure to see the top side of the figure). If the prism has an edge of 6in on its base and height of
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Question 1192228: A right, regular triangular prism has a circular cylinder inscribed in it (see figure to see the top side of the figure). If the prism has an edge of 6in on its base and height of 2in. Find the volume of the cylinder inside.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
No figure is shown; but the description is clear. The horizontal cross section of the solid shows a circle inscribed in an equilateral triangle with side length 6.
Drawing the three altitudes of the triangle divides it into 6 congruent 30-60-90 right triangles; knowing the relationship between the side lengths of those triangles shows the radius of the circle to be sqrt(3).
The volume of the cylinder is then
ANSWER: 6pi
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