Python Program THE GREAT APPLIED PROBLEM – INTRODUCTION AND BRIEF HISTORY This problem came to me when I was attending t
Posted: Sat May 14, 2022 3:42 pm
Python Program
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:
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.
Write a Python program which prompts the user for the diameter
of the tank, the length of the tank and the depth of water in the
tank. All of these measurements will be in feet. You will then
calculate the total volume of the tank, the volume of water in the
tank and how much water is required to finish filling the tank.
Some important library's to include in our program:
import math
This will allow us to use functions like math.pi
math.sin, math.cos and math.tan
we can also use:
math.asin,
math.acos and math.atan for
the inverse of sin, cos, and tan
One very important thing to know is that ALL computers work
in radiant so you will need to convert
from Rad to Deg and back again. 1rad × 180/π =
57.296°
Another thing is that there are 231 cubic
inches of water in
a gallon since we will print our three
result in gallons.
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: (I printed all of my calculations along the
way so I could ensure each was correct)
The Great Applied Problem
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 : 72.0 inches.
The length is : 192 inches.
The water depth is : 24 inches.
Central Angle Rad:
1.6821373411358607
Central Angle Degrees
96.37937020844281
Area of Sector: 4360.09998822415
Area
of Triangle:
2575.950310079758
Area of Segment: 1784.1496781443925
Volume of tank, water and required to fill
tank
The volume of the tank is:
13536.429145940354
Volume of Water: 1482.1562506962205
Water need to fill tank:
12054.272895244134
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:
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.
Write a Python program which prompts the user for the diameter
of the tank, the length of the tank and the depth of water in the
tank. All of these measurements will be in feet. You will then
calculate the total volume of the tank, the volume of water in the
tank and how much water is required to finish filling the tank.
Some important library's to include in our program:
import math
This will allow us to use functions like math.pi
math.sin, math.cos and math.tan
we can also use:
math.asin,
math.acos and math.atan for
the inverse of sin, cos, and tan
One very important thing to know is that ALL computers work
in radiant so you will need to convert
from Rad to Deg and back again. 1rad × 180/π =
57.296°
Another thing is that there are 231 cubic
inches of water in
a gallon since we will print our three
result in gallons.
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: (I printed all of my calculations along the
way so I could ensure each was correct)
The Great Applied Problem
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 : 72.0 inches.
The length is : 192 inches.
The water depth is : 24 inches.
Central Angle Rad:
1.6821373411358607
Central Angle Degrees
96.37937020844281
Area of Sector: 4360.09998822415
Area
of Triangle:
2575.950310079758
Area of Segment: 1784.1496781443925
Volume of tank, water and required to fill
tank
The volume of the tank is:
13536.429145940354
Volume of Water: 1482.1562506962205
Water need to fill tank:
12054.272895244134