Area & Volume Exploration – Component proportional changes

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Area & Volume Exploration – Component proportional changes

Question 1:         How do the Volume, Surface Area and Mass of your component vary when two key dimensions are changed but the length remains the same?

Changing one key Dimension         by  5%, 10%  &  20%

 Increasing the length: 20m

5% increase         =>   20  × 5% = 1

                                              100

        => 20m + 1m (increase) = 21m

So…  

          New cuboid dimensions =        Length = 21m

        Width         = 10m

        Height         = 5m

Volume         = 10m × 21m × 5m

        = 1050m3

S. Area        = (2×10×5)+(2×21×5)+(2×10×21)

        = 100 + 210 + 420

        = 730m3

Mass        = 7800kg/m3 × 1050m3

        = 8’190’000kg

        

This clearly shows that when the length is increased by 5% the Volume and Mass are also increased by 5%. This indicates that the Volume  and Mass are directly proportional to the length. The Surface Area would not appear to be directly proportional to the length as it does not increase by 5%.  Further exploration is needed to confirm that this proportional increase is not a one off event. I predict that the same will happen and the percentage increase will be the same for Length, Volume and Mass.

10% increase         =>   20  × 10% = 2

                                              100

        => 20m + 2m (increase) = 22m

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So…  

          New cuboids dimensions =        Length = 22m

        Width         = 10m

        Height         = 5m

Volume         = 10m × 22m × 5m

        = 1100m3

S. Area        = (2×10×5)+(2×22×5)+(2×10×22)

        = 100 + 220 + 440

        = 760m3

Mass        = 7800kg/m3 × 1100m3

        = 8’580’000kg

        

Volume         = 10m × 27m × 5m

        = 1350m3

S. Area        = (2×10×5)+(2×27×5)+(2×10×27)

        = 100 + 270 + 540

        = 910m3

Mass        = 7800kg/m3 × 1350m3

        = 10’530’000kg

        

This proves that whatever percentage one dimension is increased by, the volume and ...

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