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Truncated Cone (Posted on 2004-01-23) Difficulty: 3 of 5
If you have a truncated cone such that its upper base has a radius of a and the radius of its [larger] lower base is b, and a height h (between bases), how could you figure out its surface area using geometric reasoning?

See The Solution Submitted by Gamer    
Rating: 2.5000 (4 votes)

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Question Geometric Interpretation of Simpler Formula? | Comment 8 of 10 |
(In reply to re(3): general equation: by Richard)

To show


= pi*(a+b)*sqrt((b-a)^2+h^2)


b^2 + (h^2*b^2)/(b-a)^2 = b^2*((b-a)^2+h^2)/(b-a)^2 and

a^2 + (h^2*a^2)/(b-a)^2 = a^2*((b-a)^2+h^2)/(b-a)^2. Hence


= (pi* (b^2-a^2)/(b-a))*sqrt((b-a)^2+h^2)

= pi*(a+b)*sqrt((b-a)^2+h^2).

Thus the area of the curved part of the truncated cone can be expressed in the simpler form

pi*(a+b)*sqrt((b-a)^2+h^2) given by Ady TZIDON as well as in the form


geometrically obtained by removing a small full cone from a larger one. Is there a simple geometric interpretation for the simpler formula?
  Posted by Richard on 2004-01-26 19:06:43

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