\(a\) is inversely proportional to the cube of \(b\). When \(a=5\), \(b=2\). Find the value of \(b\) when \(\displaystyle a=\frac{5}{27}\).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6
"\(a\) is inversely proportional to \(b^{3}\)" means \(a\times b^{3}\) stays constant. The first pair of values gives the constant.
\(a\times b^{3}=5\times2^{3}=40\)
When \(\displaystyle a=\frac{5}{27}\): \(\displaystyle \frac{5}{27}\times b^{3}=40\)
\(\displaystyle b^{3}=40\times\frac{27}{5}=216\)
\(b=6\)
The value of \(b\) is 6.