- [Maximum mark: 20]
(a) Use the trapezoidal rule with five intervals, and the values given in the table, to estimate the shaded area below the curve. [3]
(b) (i) Write down the integral that represents the area of the shaded region. [2]
(ii) Hence, find the area of the shaded region. [2]
(c) Write down an equation, in terms of r and h, that shows this information. [1]
(d) Find the value of k. [4]
(e) (i) Find dA/dr. [2]
(ii) Given that A has a minimum value, find the value of r that will minimize the material used. [3]
(f) Show that the label will fit on the container. [3]