Chapter 14.5, Problem 36E

Modeling Data

A company builds a ware house with dimensions 30 feet by 50 feet. The symmetrical shape and selected heights of the roof are shown in the figure.

(a) Use the regression capabilities of a graphing utility to find a model of the form

$z=a{y}^3+b{y}^2+cy+d$

for the roof line.

(b) Use the numerical integration capabilities of a graphing utility and the model in part (a) to approximate the volume of storage space in the ware house.

(c) Use the numerical integration capabilities of a graphing utility and the model in part (a) to approximate the surface area of the roof.

(d) Approximate the are length of the roof line and find the surface area of the roof by multiplying the arc length by the length of the ware house. Compare the results and the integrations with those found in part (c).