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Geometry
Geometry

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Question 1

Calculate the area of a carpet in a model house if the real carpet has an area of 22 m2. On the scale used, 1 cm represents 0.25 m.

Answer

(a) Since 1 cm in the model represents 25 cm in real life, areas must be scaled by 25 × 25 (the area scale is 252 because the length scale is 25). So

This can be converted to square centimetres by multiplying by 100 × 100:

Alternatively, you could convert to cm2 first:

So

Question 2

A model steam engine that runs in a park is built to a scale such that 1 cm represents 0.2 m. On the model there is space in the tender for m3 of coal. What volume of coal could be carried in the real engine's tender?

Answer

Since 1 cm in the model represents 20 cm in real life, volumes must be scaled by 20 × 20 × 20.

So the volume of the tender in real life must be

Thus the volume of coal that could be carried in the real engine's tender is 40 m3.