INTEGRATION Due to an excessive amount of rain, the village dam is lling at a rate of 310(11 l 3t) litres an hour (t 2 0). The mayor is planning to evacuate the village before the dam overows, ooding the valley. The amount of water currently in the dam is 3090 000 litres and the mayor wants to know how many hours it will take for the dam to be completely full. The dam is 60 metres long, 20 metres wide and 10 metres deep. You can assume that the villagers are not using any of the dam water and there is no water loss through evaporation. (1) What is the maximum capacity of the dam in litres? (Hint: 1000 litres = 1 cubic metre) (2) Find the function that gives the number of litres in the dam at time t hours. (3) The village mayor wants to have the town evacuated before the dam is full. At what time it would the dam be full