\(a\) is inversely proportional to the cube of \(b\). When \(a=3\), \(b=2\). Find the value of \(b\) when \(\displaystyle a=\frac{8}{9}\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3
"\(a\) is inversely proportional to \(b^{3}\)" means \(a\times b^{3}\) stays constant. The first pair of values gives the constant.
\(a\times b^{3}=3\times2^{3}=24\)
When \(\displaystyle a=\frac{8}{9}\): \(\displaystyle \frac{8}{9}\times b^{3}=24\)
\(\displaystyle b^{3}=24\times\frac{9}{8}=27\)
\(b=3\)
The value of \(b\) is 3.