A water tank is in the form of an inverted frustum as shown in Figure Q5:...

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A water tank is in the form of an inverted frustum as shown in Figure Q5: The radii of the top and the bottom circles are 80 cm and 36 cm respectively. Let h cm be the height of the water in the tank at time t second (s): 80 cm. 450 36 cm. Figure Q5 (a) Express the volume V cm of the water in the tank as a function of h. Hence, find the rate of change of V in terms of h and the rate of change of h. (b) There is a hole at the bottom of the tank so that the water flows out of the tank at a rate of 200Vh cm's'. In the mean time, a water tap fills the tank at a constant rate of 600 cm's'. Find the rate of change of h as a function of h. (c) Hence, find the minimum rate of change of h. (d) A student suggests that when the rate of change of h is minimum, the volume of water in the tank is also minimum. Do you agree with the student? Explain your answer. A water tank is in the form of an inverted frustum as shown in Figure Q5: The radii of the top and the bottom circles are 80 cm and 36 cm respectively. Let h cm be the height of the water in the tank at time t second (s): 80 cm. 450 36 cm. Figure Q5 (a) Express the volume V cm of the water in the tank as a function of h. Hence, find the rate of change of V in terms of h and the rate of change of h. (b) There is a hole at the bottom of the tank so that the water flows out of the tank at a rate of 200Vh cm's'. In the mean time, a water tap fills the tank at a constant rate of 600 cm's'. Find the rate of change of h as a function of h. (c) Hence, find the minimum rate of change of h. (d) A student suggests that when the rate of change of h is minimum, the volume of water in the tank is also minimum. Do you agree with the student? Explain your answer.