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MATH125: Unit 2 Submission Assignment Answer Form
Mathematical Modeling and Problem Solving
ALL questions below regarding painting a bedroom must be answered. Show ALL step-by-step calculations, round all of your final answers correctly, and include the units of measurement
. For full credit, all explanations must be given in the spaces provided
. Upload this modified Answer Form to the intellipath Unit 2 Submission lesson. Make sure that you submit your work in a modified Microsoft Word document; scanned or handwritten work will not be accepted
. If you need assistance, please contact your course instructor.
All of the commonly used formulas for geometric objects are just the mathematical models of the characteristics of
physical objects. For example, because a basketball is approximately a sphere, it can be partially modeled by its distance
from one side through the center (
radius
, r
) and then to the other side by the diameter
formula for a sphere, D
= 2
r
.
For the two-dimensional variables of length (
L
) and width (
W
), the perimeter
and area
formulas for a rectangle are
mathematical models for the distance around a rectangle (
perimeter
, P
) and the region enclosed by the sides (
area
, A
),
respectively, as follows: P
= 2
L
+ 2
W
and A
= L
× W
Along with another variable, height (
H
), a three-dimensional rectangular prism’s volume
and surface area
can be
measured. For example, the formulas for a common closed cardboard box’s inside space (
volume
, V
) and outside
covering (
surface area
, SA
) are, respectively, as follows:
V = L x W x H
and SA = 2(L x W) + 2(W x H) + 2(L x H)
For this Submission Assignment, follow Pólya’s principles to solve your problems, as follows:
1.
Understand the problem.
2.
Devise a plan.
3.
Carry out the plan.
4.
Take a look back.
Include the following in your assignment:
Explain your interpretation of what the problem is about.
Develop and write down a strategy for solving this problem; show the steps in the correct order for your
attempted solution.
Did your strategy actually solve the problem? How do you know?
Suppose that your solution did not solve the problem—what would your next action be?
Painting a Bedroom
The walls and ceiling inside your bedroom need to be painted. To save money, you decide that you will paint the
bedroom yourself. Use the following information to solve this problem:
The bedroom is 17 feet long by 18 feet wide, and the ceiling is 9 feet high.
The inside of the bedroom door will be painted the same color as the walls.
Two coats of paint will be applied to all of the painted surfaces.
The room has one window, measuring 3 feet, 9 inches by 4 feet, which will not be painted.
Pólya’s Principle Step 1: Understand the Problem
1.
Describe in detail what you understand the problem to be. In other words, what problem will you need to solve?
Is there enough information to enable you to find a solution to your problem?
Show your work here: (10 points)
I understand the problem to be “how much of the room will I have to paint”. There is enough information to find out how much of the room I will have to paint but not enough to figure out how much it would cost to paint the room.
2.
Discuss different ways to construct the room that will be painted. Are there any restrictions on where the window and door will be located? Will the overall amount of paint that is needed change based on where these are placed in the room?
Show your work here: (10 points)
Since you are also painting the inside of the door it doesn’t matter where you put the door at all. Also the window will take up the same space anywhere you put it but it would be easier to paint around if you put it in a corner.
3.
List the facts that you know. First, find the room dimensions in feet that make a good model for this situation. One strategy would be to sketch the room as follows. Please use this model to complete the following table below. (3 points)
Side Answers
Length 17
Width
9
Height 18
4.
Using the measurements diagrammed above, label all of the rectangular faces in feet in the following table: (5 points)
Face Dimensions
Ceiling
17
18
Face Dimensions
Left Wall
18
9
Right Wall
18
9 Face Dimensions
Front Wall
17
9
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Back Wall
17
9
5.
Because all of the ending values are given in feet, find the window dimensions
in feet. Convert the length of 3 feet, 9 inches strictly into feet. The answer should be in decimal format
. Do not round
. Note that 12 inches are equal to 1 foot.
Face Dimensions
Window
3ft 9in
4ft
Show your work here: (5 points)
3x12=36in+9in. 4x12=48inc
36in+9in*48=2160in
2160/144=15 sqft Pólya’s Principle Step 2: Devise a Plan
6.
Using Pólya’s technique for problem solving, describe your plan
to solve this problem in detail. In other words, what is your solution strategy? Discuss the strategy, steps, formulas, and procedures that you will use to answer this problem.
Show your work here: (10 points)
My strategy for this was to first understand what I was solving for. Once I understood I was solving for the total
area that I would have to paint I devised a plan to find that out. First I wrote down all of the dimensions of the
room (height,width,length). After I split the dimensions into the ceiling, front wall, back wall, right wall and left
wall. I made a chart to list the dimensions of each of the parts of the room. After that I will list the dimensions of
the window because I have to find out how much of the wall I won’t have to paint. After I figure this out I can
then use the surface area formula to find out how much I would actually have to paint(
SA = 2(L x W) + 2(W x H)
+ 2(L x H)).
Pólya’s Principle Step 3: Carry out the Plan
7.
Using the formula concepts and dimensions above, find the bedroom’s total painted surface area for all of the walls
.
Show all of the calculations step by step, including the units of measurement, and round your final answer up to the nearest whole measurement
unit in the following table:
Answer
Total Painted Wall Surface Area With One Coat of Paint
630
Show your work here: (8 points)
Ceiling
Left wall:18x9ft
Right wall:18x9ft
Front:17x9ft
Back wall:17x9ft
(18x9)+(18x9)+(17x9)+(17x9)=630
8.
Do not forget to subtract the window’s area
. Also, determine the surface area for two coats by doubling the painted wall’s surface area
.
Show all of the calculations step by step, including the units of measurement, and round your final answers up to the nearest whole measurement
unit in the following table:
ANSWERS
Window’s Area
15
One Coat of Wall Paint Excluding the Window’s Area
615
Painted Wall Surface Area With Two Coats of Paint
1230
Show your work here: (8 points)
Left wall:18x9ft
Right wall:18x9ft
Front:17x9ft
Back wall:17x9ft
(18x9)+(18x9)+(17x9)+(17x9)=630(one coat)
630-15=615x2=1230ft(double coat)
9.
Using the formulas, concepts, and dimensions above, find the ceiling’s painted surface area
, including the surface areas for one and two coats.
Show all of the calculations step by step, including the units of measurement, and round your final answers up to the nearest whole measurement
unit in the following table:
Answers
Painted Ceiling Surface Area With One Coat of Paint
306
Painted Ceiling Surface Area With Two Coats of Paint
612
Show your work here: (8 points)
17x18=306x2=612
10.
Combining the answers from above, find the total painted surface area
, including both coats for the walls and ceiling.
Show all of the calculations step by step, including the units of measurement, and round your final answer up
to the nearest whole measurement
unit in the following table:
Answer
Total Painted Surface Area With Two Coats of Paint
1842ft
Show your work here: (5 points)
(17x18)+(17x18)+(18x9)+(18x9)+(17x9)+(17x9)=936-15=921ftx2=1842
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11.
Assuming that you can paint 100 square feet per hour, what will be the work time
needed to paint your bedroom?
Show all of the calculations step by step, including the units of measurement, and round your final answer off to the nearest whole hour
amount in the following table:
Answer
Painting Time for the Walls and Ceiling
18hrs
Show your work here: (8 points)
1842ft/100ft=18.42
18.42hrs
Pólya’s Principle Step 4: Take a Look Back
12.
Did this strategy actually solve the problem? How do you know? Demonstrate that your solution is correct
. In other words, explain why the values that you have created are the best times for the job. Was this the best way to solve this problem? If you had to do this again, what would you do differently? What would you do the same?
Show your work here: (10 points)
I feel like my strategy solved the problem. I used all of the given formulas to solve the problems. I feel like this way was the best to solve the problem. I got to evaluate the problem and understand it fully before I solved it. I felt like organizing the problems and creating tables and charts helped me to solve it easier. The diagram was also a huge help in solving the problem. If I had to do it again I would start earlier and analyze the question and highlight important words and sentences. I would still make the tables and charts to help me organize and still construct the diagram to help me visualize the problem.