A cylindrical tank of radius R and length L lying horizontally as in Figure 13 is filled with oil to height h.
(a) Show that the volume V(h) of oil in the tank as a function of height h is

(b) Show that

(c) Suppose that R = 2 m and L = 12 m, and that the tank is filled at a constant rate of 1.5 m³/min. How fast is the height h increasing when h = 3 m?

Transcribed Image Text:

h h)=L(R² cos ¹ (1-2)-(R-1) √2hR - IP²) h)