Question

m varies directly as cube of n. When n = 5 the value of m is 1500. Find the value of n when m = 96.

Answer 1

$$\begin{gathered} m\alpha n^3 \\ \therefore m=k{n}^3(k\mathrm{is}a\mathrm{constant}.) \\ \Rightarrow 1500=k{\left(5\right)}^3(m=1500\mathrm{when}n=5) \\ \Rightarrow 1500=125k \\ \Rightarrow k=\frac{1500}{125} \\ \Rightarrow k=12 \\ Thus,wehave: \\ m=12n^3(\mathrm{This}\mathrm{is}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{variation}.) \\ \Rightarrow 96=12n^3(\because m=96) \\ \Rightarrow n^3=8 \\ \Rightarrow n=2 \end{gathered}$$