A circular cylinder with a volume of 8pi m^3 is circumscribed about a right prism whose base is an equilateral triangle with one side that measures 2m. What is the altitude of the cylinder?

Question

accessdenied · Answer

Have you got any work on this problem done yet or are you unsure of where to begin?

anonymous · Answer

I don't know where to start

accessdenied · Answer

Ah, alright.  I think a good first step is always drawing a picture of what is being asked for.  "A circular cylinder ... circumscribed about a right prism whose base is an equilateral triangle..." and then labeling information.  Visuals often help make sense of things geometrically.

accessdenied · Answer

When it says that the cylinder is circumscribed about the right prism, it effectively means the prism fits inside the cylinder perfectly touching the interior:
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Thus the cylinder is a sort of "circumference" outside the prism.

anonymous · Answer

thank you for drawing, i drew a cylinder inside the prism

accessdenied · Answer

Yea, the language is sometimes tricky with those words!  If it had said "inscribed within", the cylinder would go inside like "in" scribed sounds like.

accessdenied · Answer

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Then we can just mark in what information is given.  Because these two figures have common points of touching, they have some relation to each other such that we can determine some information about the cylinder knowing some of the dimensions of the prism!