The scale of a map is \(1:50000\). On the map, the length of a lake is \(3.6\) cm. Calculate the real length of the lake, in kilometres.
Question 1 Report
The scale of a map is \(1:50000\).
On the map, the length of a lake is \(3.6\) cm.
Calculate the real length of the lake, in kilometres.
Answer Details
A scale of \(1:50000\) means every \(1\) cm on the map represents \(50\,000\) cm on the ground, so multiply the map length by \(50\,000\) and then convert to kilometres.
\[ 3.6 \times 50000 = 180000 \text{ cm} \] [M1]
Since \(1\) km \(=100\,000\) cm:
\[ \frac{180000}{100000} = 1.8 \]
The real length of the lake is \(1.8\) km. [A1]
Do the conversion in one clear step rather than converting to metres and losing track of a factor of \(10\). If you prefer metres as a staging post, \(180\,000\) cm is \(1800\) m, and \(1800\) m is \(1.8\) km, which agrees. Answers such as \(180\) km or \(0.018\) km come from mishandling that conversion, so always ask whether the size is realistic for a lake.
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