A microprocessor is in the shape of a cube where the sides are 5 mm in length.

  1. (i)

    Find the maximum number of microprocessors that can be placed into a container with dimensions 10 cm by 2 cm by 8 cm.

    Answer ...

  2. (ii)

    A model of the microprocessor was made to a scale of 10 : 1. Given that the surface area of microprocessor is 150 mm^2, find the surface area of the model microprocessor in square centimetres.

    Answer ... cm^2

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Worked solution

b(i)

1. Convert the container dimensions to millimetres.

Since 1 cm=10 mm1\text{ cm}=10\text{ mm},

10 cm=100 mm10\text{ cm}=100\text{ mm}, 2 cm=20 mm2\text{ cm}=20\text{ mm} and 8 cm=80 mm8\text{ cm}=80\text{ mm}.

2. Find the number of cubes that fit along each dimension and multiply.

Each microprocessor is a cube of side 5 mm5\text{ mm}.

Number that fit:
1005×205×805=20×4×16=1280.\frac{100}{5}\times \frac{20}{5}\times \frac{80}{5}=20\times 4\times 16=1280.

Answer

12801280 microprocessors

b(ii)

1. Find the surface area of the model using the area scale factor.

Scale 10:110:1 means the linear scale factor is 1010.

Area scale factor =102=100=10^2=100.

Surface area of model
=150×100=15000 mm2=150\times 100=15000\text{ mm}^2

2. Convert the model surface area from square millimetres to square centimetres.

Since 1 cm=10 mm1\text{ cm}=10\text{ mm},
1 cm2=100 mm21\text{ cm}^2=100\text{ mm}^2

15000 mm2=15000100=150 cm215000\text{ mm}^2=\frac{15000}{100}=150\text{ cm}^2

Answer

15 cm215\text{ cm}^2

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