Table 1 gives values of a continuous function g measured in centimeters at equally spaced values of x (in centimeters). The region W is bounded above by the horizontal line y=10 and below by the graph of y=g(x) for 0≤x≤6. The region is revolved about the line y=10, forming a solid.
Table 1: Values of g
x (cm)
0
1
2
3
4
5
6
g(x) (cm)
8.0
7.0
6.0
5.2
4.8
4.6
4.5
(a) For a fixed x in [0,6], write expressions for the relevant radii of the circular cross–section generated by revolving the vertical segment connecting (x,g(x)) and (x,10) about y=10. Briefly explain your reasoning.
(b) Using all of the data from Table 1 and the trapezoidal rule with six subintervals, approximate the volume of the solid. Express your answer correct to three decimal places and include appropriate units.
(c) Suppose g is known to be concave down on [0,6]. State whether the approximation in part (b) is an overestimate or an underestimate of the true volume, and justify your conclusion.