Question

Ratanpura village is situated 3 km away from Dhule district in Maharashtra state. Google maps on which they are shown is drawn to a scale of 1 : 5000.
A. Calculate the distance between the two villages in cm on the map.
B. On the map a rectangular paddy field has an area of $5c{{m}^{2}}$. Calculate the actual area of the paddy field in square meters.

Answer 1

Hint: We should note that the scale means the ratio of length on the map to that on the land. Thus this means that the scale if the scale is given as 1 : 5000, then 1 cm on the map would be equal to 5000 cm on the land. We will use this concept and solve the question.

Complete step by step answer:
In the question, it is given that a village named Ratnapura is situated 3 km away from Dhule district in the state of Maharashtra. We are further given that these places are shown on Google maps and are drawn to a scale of 1: 5000. We have been asked to find the distance between the two villages and also find the area of a paddy field. Now, before we proceed to find these values, let us know briefly what a scale is. The map scale refers to the relationship or ratio between the distance on a map and the corresponding distance on the ground. For example, a map scale of 1: 100000, means that 1 cm on the map equals 1 km on the ground. Let us now solve the two parts given in the question one by one.
A. It is given in the question that the distance between the two villages is 3 km. So, we will convert the ground distance of 3 km into the map distance of cm. We know that 1 km = 100000 cm. ( 1 km = 1000 m and 1 m = 100 cm) so, 3 km would mean,
$3\times 100000=300000cm$
So, the distance between the two villages on the map would be calculated as follows,
5000 cm on ground = 1 cm on map
300000 cm on ground = $\dfrac{1}{5000}\times 300000=60$ cm on map.
So, the distance between the two villages on the map would be 60 cm.
B. We know that the scale is 1 : 5000. So, if the area of the field on the map is given as $5c{{m}^{2}}$, then the actual area on the ground would be $5\times 5000=25000c{{m}^{2}}$. We know that 1 m = 100 cm, so we can say that $1{{m}^{2}}=\left( 100\times 100 \right)c{{m}^{2}}\Rightarrow 10000c{{m}^{2}}$, So, we can calculate the square metres as,
$10000c{{m}^{2}}=1{{m}^{2}}$ so,
$\begin{align}
  & 250000c{{m}^{2}}=\dfrac{1}{10000}\times 250000 \\
 & \Rightarrow 250000c{{m}^{2}}=25{{m}^{2}} \\
\end{align}$
So, the actual area of the paddy filed would be $25{{m}^{2}}$.

Note:
The students should be thorough with the metric system conversions as many of them end up with mistakes while doing so. It is always better to do the conversions step by step. Sometimes the students divide the value by 100 in place of 10000, while they are converting from $c{{m}^{2}}$ to${{m}^{2}}$ . So, this should be noted that it is not cm, but $c{{m}^{2}}$, so it should be $\left( 100\times 100 \right)c{{m}^{2}}$.