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
\(\frac{1}{6}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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 \(\frac{1}{8}\)
= \(\frac{1}{12}\)
Source: Myschool Past Questions Archive (Record #29385)