The height (h km) that a weather balloon can reach is related to the volume (v m₃) of helium in it at sea level by the equation:
\[h = \frac{8v^{2}}{5} – \frac{32v^{3}}{255}\ ,\ v \leq 12\]
a) Find the volume of helium required to achieve the maximum height and state this height.
[5 marks]
