How to calculate ratio part V: answers to part IV (scale drawings and maps)

Below are the answers to the questions in the hub How to calculate ratio part IV: scale drawings and maps.


Question 1

Rearrange the following map scales in order, from smallest to largest:

(1) 1 cm : 5 km
(2) 2 : 5,000
(3) 1 cm : 100 m
(4) 5 cm : 2 km
(5) 3 : 40,000

In order to make sure you're comparing like with like, you need to change all of these so that they're in ratio format, without any units. Doing this gives:

(1) 1 : 500,000
(2) 2 : 5,000 = 1 : 2,500
(3) 1 : 10,000
(4) 5 : 200,000 = 1 : 40,000
(5) 3 : 40,000 = 1 : 13,333 (to the nearest whole number)

If you rearrange these so that they go smallest to largest, you get:

(1)
(4)
(5)
(3)
(2)


Question 2

You are designing a theatre set. The actual size of the stage is 12 metres by 8 metres, and you want to create a scale drawing using a scale of 1 : 200. What are the dimensions of your scale drawing in cm?

The easiest way to deal with this is to start by converting the actual dimension of the stage to cm, which gives you 1,200 x 800 cm. To work out the dimensions of the scale drawing, just divide each dimension by 200. This gives an answer of 6 x 4 cm.


Question 3

You decide that the scale drawing you created in Question 2 isn't big enough, so you decide to create another one on a scale of 3 : 400. Again, what are the dimensions of your scale drawing in cm?

Again, use the dimensions of the actual stage in cm as your starting point. From then on, it's best to work in two steps. First step - divide by 400 to find what you'd end up with if you were using a scale of 1 : 400. Then multiply the answer by 3 to find what your dimensions would be with a scale of 3 : 400.

1,200 x 800 cm divided by 400 gives 3 x 2 cm for a model on a scale of 1 : 400

Multiplying by 3 gives dimensions of 9 x 6 cm for a model built on a scale of 3 : 400.

Question 4

A model boat enthusiast has built a scale model of his boat, which is 500 mm long.  The actual boat is 25 metres long.  What is the scale of the model?  (10 mm = 1 cm)

The scale can be written as

500 mm : 25 m

To write it as a ratio, you need to make sure you're using the same units. 

25 m = 2,500 cm = 25,000 mm

The scale you're using is therefore

500 : 25,000, which cancels down to:

5 : 250, which in turn cancels down to:

1 : 50


Question 5

The UK Ordinance Survey's "Explorer^TM" map has a scale of 1 : 25,000.  How would you express this in cm and km (e.g. "3 cm : 5 km")?

1 : 25,000 can be written as 1 cm : 25,000 cm

There are 100 cm in a metre, so you can write this as:

1 cm : 250 m

Since there are 1,000 m in a km, this in turn can be written as:

1 cm : 0.25 km

© Empress Felicity August 2010