Great Applied Problem

THE GREAT APPLIED PROBLEM INTRODUCTION AND BRIEF HISTORY

This problem came to me when I was attending the Anja S. Greer Conference on Mathematics and Technology at the Phillips Exeter Academy in New Hampshire several summers ago. The problem was presented to us as such:

A gentleman had purchased a convenience store (like a Circle K) and it came with a single pump gas station. The fuel was in a tank buried beneath the ground. I was a cylindrical tank that was lying horizontally, completely out of sight and unreachable other than an above ground pipe allowing them to add fuel and measure the depth of the tank. Its diameter was 14 feet and its length was 20 feet. The depth of the water in the tank was 4 feet. He wanted to know:

How many gallons of water were in the tank?

How many more gallons of water will it take to fill the tank?

At first I thought that this was a fairly trivial problem and that I would have his answers in a few minutes. However, when I started to reason it out, it became apparent that the solution was much more involved. After I completed the solution, I realized that this problem had more mathematics interwoven in its solution than any other mathematics problem I have ever encountered. And the best part was that it was an actual, real-life problem! Hence The Great Applied Problem was born. I held on to this problem until the end of the following school year and then presented it to my geometry students and asked them to solve it. It was a wonderful journey through all the mathematics concepts we learned throughout the year: the Pythagorean theorem, area of a triangle, area of a sector of a circle, area of a segment of a circle, right triangle trigonometry, area of a circle, volume of a cylinder, area of sectors and segments, and several instances of unit conversion. The solution of the problem also requires the students to organize their work well and to be able to logically develop a plan of problem solving.

Some important library's to include in our program:

#include #include #include #include

Since we are dealing with area of circles, sectors and segments we will be using trigonometry functions. This means we need to include our cmath and math.h

C++ has built-in trig functions for you to use: sin, cos, tan, asin, acos, atan.

Don't forget that ALL computers work in radiant so you will need to convert from Rad to Deg and back again. 1rad 180/ = 57.296

There are 231 cubic inches of water in a gallon

One last reminder - C++ does not have a built-in Pi value so use 3.14159 for Pi.

Your program prompts the user for the Diameter, Length and Water Depth. The output will be: Volume of the Tank, Volume of Water (in the tank) and How Much is Needed to fill Tank.

Sample Data:

Please enter the diameter of the tank: 12 Please enter the length of the tank: 16 Please enter the water depth of the tank: 2 The radius is: 72 inches. The length is: 192 inches. The water depth is: 24 inches. The volume of the tank is: 13536.4. Central Angles Rads: 1.68214. Central Angles Degrees: 96.3795. Area of Sector: 4360.1. Area of Triangle: 2575.95. Area of Segment: 1784.15. Volume of Water: 1482.93. Water need to fill tank: 12053.5.