19 A farmer has a water trough of length 8 m which has 1 m a semi-circular cross-section of diameter 1 m. Water is pumped into the trough at a constant rate of 0.1 m3 per minute. a Show that the volume of water in the trough is given by V - 0 - sin0, where 0 is the angle illustrated (in radians). b Find the rate at which the water level is rising at the instant when the water is 25 cm deep. Hint: First find de dh and then find at the given instant. dt