Consider the storage tank described in Question 4 of Exercises 2.2.2. Show that the volume V(h)

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Consider the storage tank described in Question 4 of Exercises 2.2.2. Show that the volume V(h) of oil when the depth is h is given by

V(h) = 32 sin (h-2) 2 + 16 + 8(h-2) (4h-h)

What is the value of h when the volume of oil is reduced to 10% of its capacity?


Data from Question 4 of Exercises 2.2.2.

An oil storage tank has the form of a circular cylinder with its axis horizontal, as shown in Figure 2.9. The volume of oil in the tank when the depth is h is given in the table below.

h/m 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 V/10001 7.3 19.7 34.4 50.3 66.1 80.9 93.9 100.5 hm Figure 2.9

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