62. Volume The head of your firm's accounting department has asked you to find a formula she can use in a computer program to calculate the year-end inventory of gasoline in the company's tanks. A typical tank is shaped like a right circular cylinder of ra- dius r and length L, mounted horizontally, as shown in the accom- panying figure. The data come to the accounting office as depth measurements taken with a vertical measuring stick marked in centimeters. a. Show, in the notation of the figure, that the volume of gaso- line that fills the tank to a depth d is c-rtd :/ VF - y² dy. V = 2L -r b. Evaluate the integral. - Measuring stick d = Depth of gasoline
62. Volume The head of your firm's accounting department has asked you to find a formula she can use in a computer program to calculate the year-end inventory of gasoline in the company's tanks. A typical tank is shaped like a right circular cylinder of ra- dius r and length L, mounted horizontally, as shown in the accom- panying figure. The data come to the accounting office as depth measurements taken with a vertical measuring stick marked in centimeters. a. Show, in the notation of the figure, that the volume of gaso- line that fills the tank to a depth d is c-rtd :/ VF - y² dy. V = 2L -r b. Evaluate the integral. - Measuring stick d = Depth of gasoline
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:62. Volume The head of your firm's accounting department has
asked you to find a formula she can use in a computer program
to calculate the year-end inventory of gasoline in the company's
tanks. A typical tank is shaped like a right circular cylinder of ra-
dius r and length L, mounted horizontally, as shown in the accom-
panying figure. The data come to the accounting office as depth
measurements taken with a vertical measuring stick marked in
centimeters.
a. Show, in the notation of the figure, that the volume of gaso-
line that fills the tank to a depth d is
c-rtd
:/ VF - y² dy.
V = 2L
-r
b. Evaluate the integral.
- Measuring stick
d = Depth of
gasoline
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