page 06 MARKS 11. On a building site, water is stored in a container. The container is a cone with diameter 180 cm at its widest point and height of 150 cm. A cross section of the cone is shown below. 150 cm 180 cm (a) Show that when the water level is at a height of h cm, 0 ≤ h ≤ 150, the volume of water in the container can be written as π 3 3 25 h V  . [The volume of a cone is given by π 2 1 3 V r h  .] Water is pumped into the container at a constant rate of 10 litres per second. (b) Find the rate at which the height is increasing when h = 125. 12. Prove by induction that, for all positive integers n, ( ) 1 1 2 2 1 1 n r n r r n       . 1 5 5