Question

The scale on a map is 1:20000
The area of a lake on the map is 1.6 square centimeters.
Calculate the actual area of the lake.
Give your answer in square meters.

Answer 1

Hint: Here, in this given question, we must first of all convert square centimeters in terms of actual measurements by using the given ratio of the on map measurements to the actual measurements, that is 1:20000. Then we must convert the obtained measurement in square centimeters in terms of square meters as asked by dividing it by the square of hundred, that is \[{{\left( 100 \right)}^{2}}=10000\] as 1 meter= 100 centimeters.

Complete step-by-step answer:
In this given question, we are first of all going to use the given ratio of the on map measurements to the actual measurements, that is 1:20000 to calculate the actual measurements as follows:
$1.6c{{m}^{2}}=1.6\times 1c{{m}^{2}}..............(1.1)$
Using the ratio 1:20000 in 1.1, we get,
$1.6\times 1c{{m}^{2}}=1.6\times {{\left( 20000 \right)}^{2}}c{{m}^{2}}=1.6\times 400000000c{{m}^{2}}=640000000c{{m}^{2}}................(1.2)$
As the actual measurement of the area of the lake.
Now, $1m=100cm$
$\Rightarrow {{\left( 1m \right)}^{2}}={{\left( 100cm \right)}^{2}}$
$\Rightarrow 1{{m}^{2}}=10000c{{m}^{2}}$…………… (1.3)
So, using equation 1.3 in the value obtained 1.2, we get,
$640000000c{{m}^{2}}=\dfrac{640000000}{10000}{{m}^{2}}=64000{{m}^{2}}................(1.4)$
Hence, we have got \[64000{{m}^{2}}\] as the actual area of the lake.
Therefore, we have got our answer as $640000000c{{m}^{2}}$ as the actual area of the lake which is equal to \[64000{{m}^{2}}\] when expressed in square meters.

Note: In this sort of questions, we must be careful to only change the units and not the numerical value while conversion of units, for example in this question 1.6 was not changed and only the $c{{m}^{2}}$ part was changed. Therefore, we should use the same numerical value with the new units to get the new value as the answer.