Question

The scale of a map is 1: 500 000.

(a) The actual distance between two towns is 172 km.

Calculate the distance, between the towns on the map.
(b) The area of a lake on the map is 12 cm^2.
Calculate the actual area of the lake in km^2​

Answer 1

let us assume that the scale is 1 cm on the map is equivalent to 500,000 cm in the real world. 500,000 cm is 5000meters or 5km. The scale can be 1cm on map is 5000 meters in real life - 1:5000. 172 km = 172000 meters. Now use ratios:

1/5000=n/172000

5000n=172000

n=34.4

The distance between the town on the map is= 34.4cm

1/5000=n/ 12cm

5000n=1200000

n=240

the actual area of the lake in km is 240

Answer 2

Given: The scale of a map is 1: 500000.

(a) The actual distance between two towns is 172 km.

(b) The area of a lake on the map is 12 cm².  

To find:

(a) The distance between the towns on the map.

(b) The actual area of the lake in km².

Solution:

• According to the scale given, 1 cm on the map is equal to 500000 km on the actual ground.

(a)

• The distance between the two towns on the map can be calculated as,

        $\frac{172}{500000} = 0.000344$

• This means that the distance between the two towns on the map is 0.000344 cm.

(b)

• If 1 cm on the map is equal to 500000 km on the actual ground, 1 cm² would be equal to,

        $(1 cm)^{2} = (500000 km)^{2}$

                    $= 25 * 10^{10} km^{2}$

• Now, the actual area of the lake can be calculated as,

        $12 cm^{2} * 25 * 10^{10} km^{2} = 3*10^{12} km^{2}$

Therefore, the distance between the towns on the map is 0.000344 cm and the actual area of the lake in km² is 3×10¹² km².