# A rectangular plot of land or area 0.45 hectare is represented on a map by a similar rectangle of area 5 cm2. Calculate R. F. of the scale of the map.

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A rectangular plot of land or area 0.45 hectare is represented on a map by a similar rectangle of area 5 cm2. Calculate R. F. of the scale of the map. Draw a scale to read upto a single metre from the map.
1. 1 : 5000
2. 1 : 8000
3. 1 : 9000
4. 1 : 3000

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Correct Answer - Option 4 : 1 : 3000

Concept:

Representative fraction:

• It represents the ratio of the number of units on the map to the number of units on the ground.
• It represents a unit-less ratio.

The representative fraction of the area is given by –

$R.F = \sqrt {\frac{a}{A}}$

Here,

a – area of the plot on the map (cm2)

A – area of the plot on the ground (cm2)

Calculation:

Given,

a = 5 cm2

A = 0.45 × 104 m2 = 4500 × 104 cm2

$\therefore R.F.\; = \sqrt {\frac{5}{{4500 \times {{10}^4}}}} = \frac{1}{{3000}}$

• The representative fraction for length is given by -

$R.F =\frac{l}{L}$

Here,

l - length of the line on the map (cm)

L - length of the line on the ground (cm)

• The representative fraction for volume is given by -

$R.F=\sqrt[3]{{\frac{v}{V}}}$

Here,

v - volume on the map (cm3)

V - volume on the ground (cm3)