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Added on: 2024-11-26 10:00:48
Order Code: SA Student Alicia Science and Maths Assignment(3_23_32241_340)
Question Task Id: 487527

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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

  • Uploaded By : Pooja Dhaka
  • Posted on : November 26th, 2024
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