2The volume of the container, V cm3, is given by = (8ℎ2 − 1 ℎ3) where h 3

cm is the height of the container.

(a)The container is heated up and its height increases from 4 cm to 4.1 cm. By using differentiation, find the approximate change in the volume of the

container. [3 marks]

(b)(i) Find the height of the container when the volume is maximum. [2 marks]

(ii) Hence, calculate the maximum volume of the container. Give your answer

in terms if . [2 marks]