Acorn Spheroform

Algebra Level 2

\[ A = \left ( \dfrac{710}{113} - \dfrac{252050}{76614} \right) R^2 \qquad \qquad V = \left( \dfrac{710}{339} - \dfrac{126025}{76614} \right) R^3 \]

Let \(A\) and \(V\) denote the area and volume of a Reuleaux triangle spheroform, respectively, where \(R\) is a parameter.

Find the value of \(R\) satisfying \( \dfrac AV = \dfrac{646}{97} \approx 6.65979\ldots \).

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