Question

A scale drawing of a car is presented in the following three scales. Order thescale drawings from smallest to largest. Explain your reasoning. (There areabout 1.1 yards in a meter, and 2.54 cm in an inch.)A. 1 in to 1 ftB. 1 in to 1 mC. 1 in to 1 yd?

Answer 1

The smallest drawing will be the one that has the smallest drawing unit with respect to the the actual unit.

We have:

A. 1 in to 1 ft

B. 1 in to 1 m

C. 1 in to 1 yd

If we put them all in meters, we have:

A. 1 in to 0.3048 m

B. 1 in to 1 m

C. 1 in to 1/1.1 = 0.90... meters

Then, the small drawing will be B, as 1 meter is the largest actual unit.

Second, will be B, that has 1 in by approximately 0.9 meters.

Third and last, option A, which drawing has an scale of 1 in in 0.3048 meters.

We can calculate the scale as a ratio between the drawing units and actual units, expressed in the same units.

For example, for A, we have:

$\frac{1\text{ in}}{1\text{ ft}}\cdot(\frac{1\text{ ft}}{12\text{ in}})=\frac{1}{12}$

So the scale is 1:12.

NOTE: look that we have cancelled all the units with this operation.

For B, we have:

$\frac{1\text{ in}}{1\text{ m}}\cdot(\frac{2.54\text{ cm}}{1\text{ in}})\cdot(\frac{1\text{ m}}{100\text{ cm}})=\frac{2.54}{100}=\frac{254}{10000}$

For C, we have:

$\frac{1\text{ in}}{1\text{ yd}}\cdot(\frac{1\text{ yd}}{3\text{ ft}})\cdot(\frac{1\text{ ft}}{12\text{ in}})=\frac{1}{36}$

You can verify that B has the smallest scale (0.0254)