smc-4608-35-Scale

Ratio, SM-Bank 054

James found a fly that was 8 mm long in real life.

Calculate the scale used in this scale drawing of the fly. (2 marks)

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\(7\ :\ 1\)

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\(\text{Scale}\)	\(=\text{Scaled length}\ :\ \text{Actual length}\)
	\(=5.6\ \text{cm}\ :\ 8\ \text{mm}\)
	\(=56\ \text{mm}\ :\ 8\ \text{mm}\)
	\(=7\ :\ 1\)

Ratio, SM-Bank 053

Oliver's bike is 1.68 metres long in real life.

Calculate the scale used in this scale drawing of Oliver's bike. (2 marks)

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\(1\ :\ 42\)

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\(\text{Scale}\)	\(=\text{Scaled length}\ :\ \text{Actual length}\)
	\(=4\ \text{cm}\ :\ 1.68\ \text{m}\)
	\(=4\ \text{cm}\ :\ 168\ \text{cm}\)
	\(=1\ :\ 42\)

Ratio, SM-Bank 052

Macton and Brownville are 15 centimetres apart on a map with a scale of \(1:150\ 000\). How far apart, in kilometres, are the two cities in real life? (2 marks)

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\(22.5\ \text{km}\)

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\(\text{Scale factor}=150\ 000\)

\(\text{Actual distance}\)	\(=\text{Scaled distance}\times \text{scale factor}\)
	\(=15\times 150\ 000\ \text{cm}\)
	\(=2\ 250\ 000\ \text{cm}\)
	\(=22.5\ \text{km}\)

Ratio, SM-Bank 051

Jinderee and Exetroll are 8 centimetres apart on a map with a scale of \(1\ :\ 2000\). How far apart, in kilometres, are the two towns in real life? (2 marks)

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\(0.16\ \text{km}\)

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\(\text{Scale factor}=2000\)

\(\text{Actual distance}\)	\(=\text{Scaled distance}\times \text{scale factor}\)
	\(=8\times 2000\ \text{cm}\)
	\(=16\ 000\ \text{cm}\)
	\(=0.16\ \text{km}\)

Ratio, SM-Bank 050

Determine the scale factor if a scaled length of 1.6 centimetres represents an actual length of 0.48 kilometres. (2 marks)

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\(30\ 000\)

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\(\text{Scale ratio}=\text{scale length}\ :\ \text{actual length}\)

\(=1.6\ \text{cm}\ :\ 0.48\ \text{km}\)

\(=1.6\ \text{cm}\ :\ 48\ 000\ \text{cm}\)

\(=1\ :30\ 000\)

\(\text{Scale factor}\)

\(=30\ 000\)

Ratio, SM-Bank 049

Determine the scale factor if an actual length of 2 centimetres represents a scaled length of 5 metres. (2 marks)

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\(\dfrac{1}{250}\)

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\(\text{Scale ratio}=\text{scale length}\ :\ \text{actual length}\)

\(=5\ \text{m}\ :\ 2\ \text{cm}\)

\(=500\ \text{cm}\ :\ 2\ \text{cm}\)

\(=500\ :\ 2\)

\(=1\ :\ \dfrac{1}{250}\)

\(\text{Scale factor}\)

\(=\dfrac{1}{250}\)

Ratio, SM-Bank 048

Determine the scale factor if an actual length of 0.3 millimetres represents a scaled length of 15 centimetres. (2 marks)

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\(\dfrac{1}{500}\)

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\(\text{Scale ratio}=\text{scale length}\ :\ \text{actual length}\)

\(=15\ \text{cm}\ :\ 0.3\ \text{mm}\)

\(=1500\ \text{mm}\ :\ 3\ \text{mm}\)

\(=500\ :\ 1\)

\(=1\ :\ \dfrac{1}{500}\)

\(\text{Scale factor}\)

\(=\dfrac{1}{500}\)

Ratio, SM-Bank 047

Determine the scale factor if an actual length of 2 millimetres represents a scaled length of 2 metres. (2 marks)

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\(\dfrac{1}{1000}\)

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\(\text{Scale ratio}=\text{scale length}\ :\ \text{actual length}\)

\(=2\ \text{m}\ :\ 2\ \text{mm}\)

\(=2000\ \text{mm}\ :\ 2\ \text{mm}\)

\(=1000\ :\ 1\)

\(=1\ :\ \dfrac{1}{1000}\)

\(\text{Scale factor}\)

\(=\dfrac{1}{1000}\)

Ratio, SM-Bank 046

Determine the scale factor if a length of 3 centimetres on a map represents an actual length of 2.4 kilometres. (2 marks)

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\(80\ 000\)

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\(\text{Scale ratio}\)

\(=3\ \text{cm}\ :\ 2.4\ \text{km}\)

\(=3\ \text{cm}\ :\ 240\ 000\ \text{cm}\)

\(=1\ :\ 80\ 000\)

\(\text{Scale factor}\)

\(=80\ 000\)

Ratio, SM-Bank 045

Determine the scale factor if a length of 5 millimetres on a map represents an actual distance of 20 metres. (2 marks)

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\(4000\)

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\(\text{Scale ratio}\)

\(=5\ \text{mm}\ :\ 20\ \text{m}\)

\(=5\ \text{mm}\ :\ 20\ 000\ \text{mm}\)

\(=1\ :\ 4000\)

\(\text{Scale factor}\)

\(=4000\)

Ratio, SM-Bank 044

A model train is built using a scale of \(4:20\ 000\).

For each of these actual lengths, find the scaled length.

\(40\ \text{m}\) (1 mark)

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\(87\ 450\ \text{cm}\) (1 mark)

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\(2400\ \text{m}\) (1 mark)

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a. \(\text{8 mm or 0.8 cm}\)

b. \(\text{17.49 cm or 0.1749 m}\)

c. \(\text{48 cm or 0.48 m}\)

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\(\text{Scale}\ \rightarrow\ 4:20\ 000=1:5000\)

a.	\(\text{Scaled length }\)	\(\dfrac{40}{5000}\ \text{m}=\dfrac{40\ 000}{5000}\ \text{mm}\)
		\(=\text{8 mm}=\text{0.8 cm}\)

b.	\(\text{Scaled length}\)	\(=\dfrac{87\ 450}{5000}\ \text{cm} \)
		\(=\text{17.49 cm}=\text{0.1749 m}\)

c.	\(\text{Scaled length}\)	\(=\dfrac{2400}{5000}\ \text{m}=\dfrac{240\ 000}{5000}\ \text{cm}\)
		\(=\text{48 cm}=\text{0.48 m}\)

Ratio, SM-Bank 043

The scale on a map is \(4:20\ 000\).

For each of these scaled distances, find the actual distances in kilometres.

\(2\ \text{cm}\) (1 mark)

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\(5\ \text{mm}\) (1 mark)

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\(18.4\ \text{cm}\) (1 mark)

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a. \(100\ \text{m or } 0.1\ \text{km}\)

b. \(40\ \text{m or } 0.04\ \text{km}\)

c. \(920\ \text{m or } 0.92\ \text{km}\)

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\(\text{Scale}=4:20\ 000=1:5000\)

a.	\(\text{Actual Distance}\)	\(=2\ \text{cm}\times 5000 \)
		\(= 10\ 000\ \text{cm}\)
		\(=100\ \text{m}=0.1\ \text{km}\)

b.	\(\text{Actual Distance}\)	\(=8\ \text{mm}\times 5000 \)
		\(=40\ 000\ \text{mm}\)
		\(=40\ \text{m}=0.04\ \text{km}\)

c.	\(\text{Actual Distance}\)	\(=18.4\ \text{cm}\times 5000 \)
		\(= 92\ 000\ \text{cm}\)
		\(=920\ \text{m}=0.92\ \text{km}\)

Ratio, SM-Bank 042

The scale on a map is \(1:10\ 000\).

For each of these scaled distances, find the actual distances in kilometres.

\(3\ \text{cm}\) (1 mark)

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\(8\ \text{mm}\) (1 mark)

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\(24.3\ \text{cm}\) (1 mark)

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a. \(300\ \text{m or } 0.3\ \text{km}\)

b. \(80\ \text{m or } 0.08\ \text{km}\)

c. \(2430\ \text{m or } 2.43\ \text{km}\)

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a.	\(\text{Actual Distance}\)	\(=3\ \text{cm}\times 10\ 000 \)
		\(= 30\ 000\ \text{cm}\)
		\(=300\ \text{m}=0.3\ \text{km}\)

b.	\(\text{Actual Distance}\)	\(=8\ \text{mm}\times 10\ 000 \)
		\(= 80\ 000\ \text{mm}\)
		\(=80\ \text{m}=0.08\ \text{km}\)

c.	\(\text{Actual Distance}\)	\(=24.3\ \text{cm}\times 10\ 000 \)
		\(= 243\ 000\ \text{cm}\)
		\(=2430\ \text{m}\)
		\(=2.43\ \text{km}\)

Ratio, SM-Bank 035 MC

The actual body length of a beetle Brad has caught is 24 mm.

A scale drawing of the beetle is shown below.

What scale is used in the drawing?

\(1 \text{cm represents } 5\ \text{mm}\)
\(1 \text{cm represents } 2\ \text{mm}\)
\(2 \text{cm represents } 1\ \text{mm}\)
\(5 \text{cm represents } 1\ \text{mm}\)

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\(B\)

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\(\text{Scale:}\)

\(12\ \text{cm}: 24\ \text{mm}\)

\(=120\ \text{mm}: 24\ \text{mm}=5:1\)

\(\text{In the options given, the ratio of}\ 5 : 1\ \text{occurs when}\)

\(\text{10 mm represents 2 mm}\ \textbf{OR}\ \text{when 1 cm represents 2 mm}\)

\(\Rightarrow B\)

Ratio, SM-Bank 034 MC

This picture shows a stone vase.

The picture is 2 cm high. The actual vase is 40 cm high.

What scale is used in the picture?

\(\text{2 cm represents 20 cm}\)
\(\text{4 cm represents 40 cm}\)
\(\text{1 cm represents 2 cm}\)
\(\text{1 cm represents 20 cm}\)

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\(D\)

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\(\text{Scale:}\ \ 2\ \text{cm}\ :\ 40\ \text{cm}\)

\(\rightarrow \text{Divide both sides by }2\)

\(\text{Scale:}\ \ 1\ \text{cm}\ :\ 20\ \text{cm}\)

\(\Rightarrow D\)

Ratio, SM-Bank 033 MC

Two places are 5.4 cm apart on a map.

On the map 1 cm represents 4 km.

What is the actual distance between the two places?

\(1.08\ \text{km}\)
\(10.8\ \text{km}\)
\(21.6\ \text{km}\)
\(43.4\ \text{km}\)

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\(C\)

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\(\text{Actual distance}\)	\(=5.4\times 4\)
	\(=21.6\ \text{km}\)

\(\Rightarrow C\)

Ratio, SM-Bank 029 MC

A television broadcasting tower is 800 metres high.

A model of the tower is built with a scale of 1 : 4000.

What is the height of the model?

\(5\ \text{cm}\)
\(20\ \text{cm}\)
\(200\ \text{cm}\)
\(320\ \text{cm}\)

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\(B\)

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\(\text{Model height}\)	\(=\dfrac{800}{4000}\)
	\(= 0.2\ \text{m}\)
	\(= 20\ \text{cm}\)

\(\Rightarrow B\)