Rework Exercise 41 for a situation with spill thickness

(T and r in feet) and radius of containment 9 feet.

Data from Exercises 41

A ruptured pipe in an offshore oil rig produces a circular oil slick that is T feet thick at a distance r feet from the rupture, where

At the time the spill is contained, the radius of the slick is 7 feet. We wish to find the volume of oil that has been spilled.

a. Sketch the graph of T(r). Notice that the volume we want is obtained by rotating the curve T(r) about the T axis (vertical axis) rather than the r axis (horizontal axis).

b. Solve the equation

for r in terms of T. Sketch the graph of r(T), with T on the horizontal axis.

c. Find the required volume by rotating the graph of r(T ) found in part (b) about the T axis.

Transcribed Image Text:

T(r) 2 1 + p2