Answer :
To determine the actual area of the mine based on the given scale and the measured area, we can follow these steps:
Understanding the Scale: The scale given is 1:2000, which means 1 unit on the map represents 2000 units in actual size.
Planimeter Measurement: The area measured by the planimeter is 58 cm². This is the area on the map or the plotted area.
Converting Map Area to Actual Area:
Since the map is at a scale of 1:2000, each linear dimension on the map is 1/2000th of the actual size. Therefore, the area is scaled by the square of this factor.
The conversion factor for the area is [tex](2000)^2 = 4,000,000[/tex].
Therefore, the actual area [tex]A[/tex] in cm² is calculated as:
[tex]A = 58 \text{ cm}^2 \times 4,000,000 = 232,000,000 \text{ cm}^2[/tex]
Converting cm² to m²:
There are 10,000 cm² in 1 m². To convert cm² to m², divide by 10,000.
- So,
[tex]\frac{232,000,000 \text{ cm}^2}{10,000} = 23,200 \text{ m}^2[/tex]
- So,
Selecting the Correct Multiple Choice Option:
The actual area of the mine in m² is 23,200. Hence, the correct answer is:
Option (c) 23200.
