Question

On a map of scale 1:20000 the area of a forest is 50cm^2.On another map the area of the forest is 8cm^2.Find the scale of the second map.Explain in an easy way Pleas

Answer 1

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on a map of scale 1:20000 the area of forest is 50 cm sq. On another map the area of forest is 8cm sq .find the scale of the second map.

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Student Answers

WILLIAM1941 | STUDENT

This question can be solved as follows.

On the first map the scale is 1:20000 and the area of the forest is 50 cm^2.

With a scale of 1:20000, a unit length on the map represents a length of 20000. 1 cm^2 = 1 cm* 1 cm which represents 20000*20000 cm^2 = 4*10^8 cm^2

50 cm^2 represents 4*50*10^8 cm^2 = 200* 10^8 cm^2

Now on the other map the same 200* 10^8 is represented by 8 cm^2. So the scale is sqrt [ 200* 10^8 / 8 ] = sqrt [ 25* 10^8 ] = 5* 10^4 = 50000.

Therefore the scale on the second map is 1: 50000.

Answer 2

The scale of the second map which has the area of the forest as 8cm² is 1:50000 .

Area of the forest on the map = 50 cm²

The scale of the map = 1:20000

We know that the scale of the map is defined on the area as:

$\text { (scale) ^2}$$\text{(scale)^2}x^{2}$$\text {(scale)}^2=\text{map area}\div \text{original area}$

Now we will use this to calculate the original area on the map.

Let the original area be A.

$or, (\frac{1}{20000} )^2=\frac{50}{A}\\ \\or, A = 20000^2\times 50\\\\or, A=2\times 10^{10} \text { m}^2$

Now we will use this original area of the forest to calculate the scale of the second map.

This forest on the second map covers an area of 8 cm²

Let the scale of the second map be $1:y$ .

Therefore using the above equation we get:

$(\frac{1}{y} )^2=\frac{8}{2\times 10^{10}} \\\\or,(\frac{1}{y} )^2=\frac{4}{10^{10}}$

$or,(\frac{1}{y} )=\sqrt{\frac{4}{10^{10}}}\\\\or, \frac{1}{y}=\frac{2}{10^5} \\\\or, \frac{1}{y}=\frac{2}{100000} \\\\or, \frac{1}{y}=\frac{1}{50000} \\\\or, 1:y=1:50000$

Hence the required scale for the second map is 1:50000 .

Learn more about scale of a map at:

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