The function y = 4 − (x2/4) on the interval [0, 4] is revolved about the line y = b. (a) Find the volume of the resulting solid as a function of b. (b) Use a graphing utility to graph the function in part(a), and use the graph to approximate the value of b that minimizes the volume of the solid. (c) Use calculus to find the value of b that minimizes the volume of the solid, and compare the result with the answer to part (b).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

The function y = 4 − (x2/4) on the interval [0, 4] is revolved about the line y = b.

(a) Find the volume of the resulting solid as a function of b.

(b) Use a graphing utility to graph the function in part(a), and use the graph to approximate the value of b that minimizes the volume of the solid.

(c) Use calculus to find the value of b that minimizes the volume of the solid, and compare the result with the answer to part (b).

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