Really basic question about enlargements?

skyscraperblue

I keep getting a different number of zeros than the book says every time I do this question, can someone point out my mistake?

Q:
The Eiffel Tower is 300m high. A model of the Eiffel Tower is 15cm high and its base area is 25.5 sq cm. What is the base area of the actual tower?

Michael Collins

Let us assume that every dimension is scaled in the same ratio as the height i.e. the model is scaled down from the actual tower by a factor of 300/0.15 = 2,000 - for each dimension.

Since the area of the base is the product of two dimensions (length by width) we must multiply by 2,000 - twice:

Actual tower base area

[latex] (2000)(2000)(25.5)\;\hbox{cm}^2[/latex]

[latex] =102 \times 10^6\;\hbox{cm}^2[/latex]

We can convert to square metres:

[latex] 1\;\hbox{cm} = 10^{-2}\;\hbox{m} [/latex]

[latex] 102 \times 10^6\;\hbox{cm}^2=102 \times 10^6\;(10^{-2}\hbox{m})^2 = (102 \times 10^6) (10^{-4})\;\hbox{m}^2 = 102 \times 10^2\;\hbox{m}^2 = 10,200\;\hbox{m}^2 = 1.02\;\hbox{ha}[/latex]

where "ha" is the symbol for hectares.