T varies inversely as the cube of R. When R = 3, T = 281 2 81 , find T when R = 2

Assessment: JAMB UTME - Mathematics - 2011 Subject: General Mathematics

Question 1 Report

T varies inversely as the cube of R. When R = 3, T = $\frac{2}{81}$ , find T when R = 2

\frac{1}{18}

\frac{1}{12}

\frac{1}{24}

\frac{1}{6}

Answer Details

T $α \frac{1}{R^{3}}$
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 $\frac{1}{8}$
= $\frac{1}{12}$

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