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IA1 Building a Shed
Formulate a Solution
Problem Definition
Build a backyard shed for storage
Problem Motivation
We need a shed for storage and a workshop
Problem Analysis
Get a scale map of the yard from google maps
Calculate a scale for a more enlarged map
Draw a scale image of the shed on the scale map
Calculate volume of soil removed for shed slab
Assumptions
I have no slope in the yard
Scale used in google maps is accurate
Limitations
Cost I have a budget of $1000
My scale diagram will have limited accuracy (maybe accurate to 10cm)
Conditions
Have a slab with a minimum of 50mm edge greater than the shed
Observations
A big tree needs to be removed before building
Variables
Period flooding of back yard
-336550281940234940722224150metres
0050metres
Mathematical Model
3489594130810House
00House
349031313081000781291130684tree
tree
456532611959800
1214120124460Slab edge
00Slab edge
16205208572501655264123667Proposed Shed
6m x 4m
Proposed Shed
6m x 4m
30124401047754.1metres
004.1metres
3202789276559Scale 1: 294
Scale. ______. = 20metres
Scale 1: 294
Scale. ______. = 20metres
19548041200416.1metres
006.1metres
15285848476Garden
Garden
Solution Plan
Calculate map Scale
determine a scale for a map of my property
Draw shed, slab, gardens on map to scale
calculate volume of dirt to be excavated
calculate perimeter of slab for boxing
Calculate area for garden
Solve the Problem
Calculate map scale
from my google map I measured 20m = 10mm and my yard is 50 m long. So 17cm = 50m
Therefore the scale is
17cm = 5000cm
So my scale is
1 : 294
Determine scale for map of my property
(see mathematical model)
Calculate the volume of soil.
Volume of rectangular prism = L x W x H
= 6.1m x 4.1m x 0.1m
=2.5 m3
Summary of the solution
After determining a scale for my map and drawing in the shed and slab, I found I needed to excavate 2.5m3 of soil for the slab. So I need to buy 2.5 metres of concrete and lay it in the boxing. The amount of boxing required is .
Evaluate/Verify the Solution
Reasonableness
If I measure off the printed version of my scale model I find that a scale of 1:294 gives me a shed size (measured 22mm off the model) of 6.468metres which is very close to my shed size of 6.1 metres. This is a 6100 6468 = 93.4% so I am within a 6% accuracy.
This is reasonable but I would go back and double check my scale again and my measurement of the shed from the printed model diagram.
Validity of solution
I would judge the solution and model to be valid as it gives logical and fairly accurate results when I measure the model of the shed and then use the scale to calculate the real life size. It is valid because the model is based on scale mathematics.
Utility of model
The model is effective as can be seen from the results above.
Limitations difficult to get fractional parts of a millimetre when measuring lengths on the model. This means I could be in error by +- 294mm.
Strength I can easily measure dimensions of the shed and adjust as required.
Conclusions
Conclusions
I have designed a shed that fulfills the specifications of the problem. Ie. The shed is large enough for a workshop and storage. However I have blown the budget as the slab will cost at least $1000 by itself. My budget overrun is $________.
Amendments/justification of model
The model is only accurate to +- 294mm. To make the model more accurate I could use a larger scale diagram or I could use technology such as a technical drawing graphics package (eg. Solidworks) but this would mean money to buy it and time to master it.
Future recommendations for solving the problem
Definitely need more money for the budget or I need to go back and redesign a much smaller shed and work out costs if I do a lot of the work myself.
Appendix
Possible shed proposal