1.43: Past-paper question 5

4PM1/2/November/2024 — Question 5 · 5 marks

The height of liquid in a vessel P\displaystyle P is h\displaystyle h
The volume, V\displaystyle V, of the liquid in P\displaystyle P is given by V=6h3\displaystyle V = 6h^3
Liquid is leaking from P\displaystyle P at a constant rate of 36cm3/s\displaystyle 36 \mathrm{cm}^3/\mathrm{s}
Find the exact rate of change, in cm/s\displaystyle \mathrm{cm}/\mathrm{s}, of h\displaystyle h when V=384cm3\displaystyle V = 384 \mathrm{cm}^3
(5)