Maps and Scales

Ratio and Proportion

Maps and Scales

What we have covered so far...

• converting scales with units to Scale Ratios

• converting Scale Ratios to scales with units

• Using both Scale Ratios and scales with units to find unknown and solve problems

• Convert length/distance ratios to area ratios

• Using both Area Ratios to find unknown and solve problems

Length Ratio

The scale of a map is known to be 1 : 500 000. Find the actual distance between a mall and the bus interchange if the represented distance on the map is 3.2 cm.
 $1:500\ 000$  
 $1\ cm\ :\ 500\ 000\ cm$  
 $1\ cm\ :\ 5\ km$  
 $\times3.2\circ\circ\times3.2$  
 $3.2\ cm\ :\ 16\ km$  
Ans : 16 km

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Q1 Given that 2 cm represented 5 km on a certain map, find the scale of the map. Give the answer in the form 1:k.

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Find the actual distance between two police stations that are 6.6 cm apart on the map using the ratio 1:k found in the previous part. Give your answer in km.

Area Ratio

Given that the scale of a map is 1 : 30 000, find the actual area occupied by a building if the represented building area on the map is 2.7 $cm^2$  .

 $1\ :\ 30\ 000$  
 $1\ cm\ :\ 30\ 000\ cm$  
 $1\ cm\ :\ 0.3\ km$   $1^2\ cm^2\ :\ 0.3^2\ km^2\ <--Area\ ratio$  
 $1\ cm^2\ :\ 0.09\ km^2$  
 $\times30\circ\circ\times30$  
 $30\ cm^2\ :\ 2.7\ km^2$  
Ans : 30  $cm^2$ 

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Find the distance between two libraries as represented on the map if they are actually 9 km apart on the ground. Give your answer in cm.

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Q2 The scale of a map is 1 : 40000.

If the road is represented as 2.5 cm on the map, find the actual length of the road, in km.

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If the actual area of a plot of land is 0.5 km², find the area of the represented plot on the same map, in cm². (Give the answer without units)

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2cm on a certain Map A represents 2.5 km. Write this scale in the form 1:n.

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The area of a park on Map A is 32 cm², calculate the actual area of the park in km². (Give the answer without units)

Did you use 1:125000 for the previous qn?

• Here is an alternative

• 2 cm : 2.5 km

• 2² cm² : 2.5² km²

• 4 cm² : 6.25 km²

• x8 $\cdot\cdot\cdot$  x8

•  $32\ cm^2:\ 50\ km^2$  

Fill in the Blanks

Hence, calculate the area, in cm², of the same park on another Map B, which has a scale of 1 : 500 000.

So did you manage to get 50 km²?

• Does the actual size of the park change? [invariance]

• What do you keep constant if you need to do calculation involving change of scale?

So that concludes

the Quizizz segment