Acorn Spheroform

Algebra Level 2

A = ( 710 113 − 252050 76614 ) R 2 V = ( 710 339 − 126025 76614 ) R 3 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 A and V V denote the area and volume of a Reuleaux triangle spheroform , respectively, where R R is a parameter.

Find the value of R R satisfying A V = 646 97 ≈ 6.65979 … \dfrac AV = \dfrac{646}{97} \approx 6.65979\ldots .


The answer is 1.

W Rose by W Rose , 63, USA

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1 solution

Hung Woei Neoh
Jul 13, 2016

Area = ( 710 113 − 252050 76614 ) R 2 ≈ 2.9933 R 2 =\left(\dfrac{710}{113}-\dfrac{252050}{76614}\right)R^2\approx 2.9933R^2

Volume = ( 710 339 − 126025 76614 ) R 3 ≈ 0.4495 R 3 =\left(\dfrac{710}{339}-\dfrac{126025}{76614}\right)R^3\approx 0.4495R^3

Area ÷ \div Volume = 6.6598 =6.6598

2.9933 R 2 0.4495 R 3 = 6.6598 6.6592 R = 6.6598 R = 6.6592 6.6598 ≈ 0.9999 ≈ 1 \dfrac{2.9933R^2}{0.4495R^3}=6.6598\\ \dfrac{6.6592}{R}=6.6598\\ R=\dfrac{6.6592}{6.6598}\approx0.9999\approx\boxed{1}

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