Question

Mr. Dunson made a model of a skyscraper that was 10 in. high. If Mr. Dunson used the scale of 2 inches represents 12 feet, what would be the height of the actual skyscraper?

Answer 1

Answer:

The scale is 4.2 feet to 525 metres. (

4.2

ft :

525

m)

Normally a scale is stated as a proportion (without units) so both measurements must be in the same units so that they cancel.

It is possible to do this in 2 ways, by converting 4.2 feet to metres, or by converting 525 m to feet. The final result will be the same in both cases.

Let's convert to metres.

1ft

=

0.3048

m

So the model is

4.2

⋅

0.3048

=

1.28016

m tall.

Scale is

1.28016

:

525

This is not very useful, so lets divide by 1.28016 both sides to get 1 on the LHS (this does not change the proportion).

1.28016

1.28016

:

525

1.28016

gives

1

:

410.10498687

...

Still doesn't look useful, and is way more precise than we can possibly measure the model to.

Most architectural models are made of cardboard or plastic foam, which is not normally cut to greater accuracy than about 1mm, which in this case is

0.001

1.28016

⋅

100

1

%

≈

0.08

%

.

If the model is made to simply give an idea of what the building will look like then it may be misleading to put a highly accurate scale on it.

It is much more useful to use integers, and it is not reasonable to use a scale which is more precise than can be built or measured, so let's round the answer.

1

:

410

(or possibly even

1

:

400

) would be accurate enough in most cases. It gives a viewer an idea of how big the real thing would be.

If the model was made (and could be measured) accurately, then

1

:

410

would be a good choice.

Note: If the model is in fact a computer model then much higher accuracy would be appropriate, because the viewer can usually get very accurate dimensions from the model very easily.

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