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 (cm^{2})

A – area of the plot on the ground (cm^{2})

__Calculation__:

Given,

a = 5 cm^{2}

A = 0.45 × 10^{4} m^{2} = 4500 × 10^{4} cm^{2}

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

- 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 (cm^{3})

V - volume on the ground (cm^{3})