\[
d \propto h^{2}
\]
Given that $d=80$ when $h=5$, work out the value of $d$ when $h=3$
Give any decimal answers to 1 d.p.
Answer
Final Answer: The value of \(d\) when \(h=3\) is \(\boxed{28.8}\).
Step 1 ：Given that \(d \propto h^{2}\), we can express this relationship as \(d = k \cdot h^{2}\), where \(k\) is the constant of proportionality.
Step 2 ：We are given that \(d=80\) when \(h=5\). Substituting these values into the equation gives us \(80 = k \cdot 5^{2}\). Solving for \(k\) gives us \(k = \frac{80}{5^{2}} = 3.2\).
Step 3 ：Now that we have the value of \(k\), we can find the value of \(d\) when \(h=3\). Substituting these values into the equation gives us \(d = 3.2 \cdot 3^{2} = 28.8\).
Step 4 ：Final Answer: The value of \(d\) when \(h=3\) is \(\boxed{28.8}\).
