T varies inversely as the cube of R. When R = 3, T = \(\frac{2}{81}\), find T when R = 2
A. \(\frac{1}{18}\) B. \(\frac{1}{12}\) C. \(\frac{1}{24}\) D. \(\frac{1}{6}\)
Correct Answer: B
Explanation
T \(\alpha \frac{1}{R^3}\) T = \(\frac{k}{R^3}\) k = TR3 = \(\frac{2}{81}\) x 33 = \(\frac{2}{81}\) x 27 dividing 81 by 27 k = \(\frac{2}{2}\) therefore, T = \(\frac{2}{3}\) x \(\frac{1}{R^3}\) When R = 2 T = \(\frac{2}{3}\) x \(\frac{1}{2^3}\) = \(\frac{2}{3}\) x \(\frac{1}{8}\) = \(\frac{1}{12}\)
