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 radius r and length L, mounted horizontally, as shown in the accompanying 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 gasoline that fills the tank to a depth d is

b. Evaluate the integral.

Transcribed Image Text:

V = 2L p=r+d -r Vr² - y² dy.