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A block of land has an area of 4000 m².
When represented on a map, this block of land has an area of 10 cm².
On the map 1 cm would represent an actual distance of
A. `10\ text(m)`
B. `20\ text(m)`
C. `40\ text(m)`
D. `400\ text(m)`
E. `4000\ text(m)`
`B`
`text(Area scale factor) = k^2`
| `k^2` | `= 4000/10` |
| `= 400` | |
| `:. k` | `= sqrt(400)` |
| `= 20` |
`:.\ text(Linear scale factor) = 20,`
`text(i.e.)\ \ 1\ text(cm):20\ text(m)`
`=> B`
The scale used on a map is `1:50\ 000`.
On this map, a distance of 4 km would be represented by
A. `2.0\ text(cm)`
B. `5.0\ text(cm)`
C. `8.0\ text(cm)`
D. `12.5\ text(cm)`
E. `20.0\ text(cm)`
`C`
`text(Map scale is)\ 1:50\ 000`
`∴\ text(On the map, 4 km)`
`= 4000/(50\ 000)\ text(m)`
`= 0.08\ text(m)`
`= 8\ text(cm)`
`=> C`