Question

In a model of a soccer field, the length of the field is $10\text{inches}.$ If the actual length of the football field is $100\text{yards},$ find the scale factor used to draw the model.

• A. $\frac{1}{10}$
• B. $\frac{1}{360}$
• C. $\frac{1}{3600}$
• D. None of the above

Answer 1

The correct option is B $\frac{1}{360}$

$\text{Given:}$
$\bullet$ Length in the model = $10\text{inches}$
$\bullet$ Actual length = $100\text{yards}$

$\because$ $1$ yard = $36\text{inches}$
$\therefore$ Actual length $=100\times 36=3600\text{inches}$

We know that,

$\text{Scale factor}$

= $\frac{\text{Dimension of scale model}}{\text{Dimension of actual object}}$

= $\frac{10\text{inches}}{\text{3600 inches}}$

= $\frac{1}{360}$

Hence, option (b.) is correct.