Math: Tank - Cone - Ice - Graph

ENG1063 Engineering Mathematics

Questions:

i) A rectangular water tank (see in the figure below) is being filled with water at a constant rate of 20 litres per second. If the base of the tank is 1 metre wide and 2 metres long, determine the rate of change in the height of the water in the tank. Express your answer in cm / sec).

ii) The total surface area S of a cone of base radius (r) and perpendicular height (h) is given by the following equation:

If (r) and (h) are each increasing at the rate of 0.25 cm/sec, find the rate of change that S is increasing at the instant when r = 6cm and h = 8cm, expressing your answer in cm2 per second.

iii) A large sheet of ice in the shape of a circle, has an initial radius of 350 miles. If the ice shrinks at the rate of 1.5 miles per year, determine the rate at which the ice is shrinking.

iv) Two quantities Q and H are believed to be related by the equation Q= kHn. The values obtained for Q and H shown in the table below were obtained during an experiment.

Plotting the values of Q and H using graph paper or computer graphing software show the relationship between Q and H and determine;

a. the gradient of the curve from your graph,

b. the law connecting Q and H, expressing the law that you have determined in the form of an equation.

c. The average rate of change for both Q

v) Use the function of a function rule to determine the rate of change of volume of a sphere which is being filled by water. You should use the following data for your answer:

a) Radius of water changes at 0.6 cms-1

b) Radius of sphere = 6 cm.

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