Hi ...A scale model of a building has a roof area of 32cm^2. The scale factor is 1:250. Whats the actual roof area in square metres?
Thanks..
Hi Neverquit,
The important thing to remember is that a model length L represents real length 250L, but a model area A represents real area (250^2)A. This is apparent if we write
$\displaystyle 1=\frac{1\ \text{model cm}}{250\ \text{real cm}}$
and square both sides. (For some reason, during my studies this was emphasized most in chemistry, not so much math or other sciences.)
$\displaystyle 32\ (\text{model cm})^2 = 32\ (\text{model cm})^2 \cdot \left(\frac{250\ \text{real cm}}{1\ \text{model cm}}\right)^2$
$\displaystyle = 32\ (\text{model cm})^2 \cdot \frac{62500\ (\text{real cm})^2}{1\ (\text{model cm})^2} = 2000000\ (\text{real cm})^2 = 200\ (\text{real m})^2$