# Optimum radius and height of frustum of right circular cone with set volume?
Asked Jul 16, 2017, 09:36 PM
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| I have worked out how to find the optimum surface area dimensions for a full cone with a set volume, but am unsure how to go about this when the cone is truncated (bottom pointed end cut off).
I've derived the below volume and surface area formulas for a frustum cone.
V = ⅓.Pi.h(R^2 + Rr + r^2)
SA = Pi(R + r)[(R-r)^2 + h^2]^½
I then found what h = using the first volume formula:
h = (3V)/Pi(R^2 + Rr + r^2)
Then I subbed h into the SA formula such that:
SA = Pi(R + r)[(R-r)^2 + (3V/Pi(R^2 + Rr + r^2))]^½
I think that I am supposed to use differential calculus now to find the critical values/local minimum but am not sure how to do this because there are two different radii values? | ##
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