3
\includegraphics[max width=\textwidth, alt={}, center]{f759ce41-708e-4fe7-80b9-adc2be2972ac-04_489_465_258_840} The diagram shows a water container in the form of an inverted pyramid, which is such that when the height of the water level is \(h \mathrm {~cm}\) the surface of the water is a square of side \(\frac { 1 } { 2 } h \mathrm {~cm}\).

1. Express the volume of water in the container in terms of \(h\).
   [0pt] [The volume of a pyramid having a base area \(A\) and vertical height \(h\) is \(\frac { 1 } { 3 } A h\).]
   Water is steadily dripping into the container at a constant rate of \(20 \mathrm {~cm} ^ { 3 }\) per minute.
2. Find the rate, in cm per minute, at which the water level is rising when the height of the water level is 10 cm .
   \includegraphics[max width=\textwidth, alt={}, center]{f759ce41-708e-4fe7-80b9-adc2be2972ac-06_403_773_258_685} In the diagram, \(A B = A C = 8 \mathrm {~cm}\) and angle \(C A B = \frac { 2 } { 7 } \pi\) radians. The circular \(\operatorname { arc } B C\) has centre \(A\), the circular arc \(C D\) has centre \(B\) and \(A B D\) is a straight line.