An oil tank has the shape of a cylinder with a diameter of 10 feet. It is mounte
ID: 2836117 • Letter: A
Question
An oil tank has the shape of a cylinder with a diameter of 10 feet. It is mounted so that the axis of the cylinder is horizontal (the circular cross-sections of the cylinder are vertical). If the depth of the oil is 6 feet, what percentage of the total capacity of the tank is filled? After drawing a picture and setting up this problem, use the following methods to find a numerical estimate and answer.
a. Use geometric techniques to estimate the percentage full. Find an upper and lower bound to the percentage full.
b. Express the area (and so the percentage) in terms of an elementary integral, then obtain an approximate numerical value for this integral using one of the two integration functions on your computer.
c. Use analytical methods to evaluate the integral in part a analytically.
d. How do your two answer compare with each other and yor original estimate?
Explanation / Answer
You are indeed correct. ted has right approach, but wrong equation.
Since diameter = 10, then radius = 5, so equation of circle is:
x