Q5: A map is drawn to a scale of 1 : 25000: 13 (a) Two villages are 4.5km apart. Calculate in cm, their distance apart on the map. (b) A housing estate drawn on the map occupies an area of 40cm? Calculate the actual area of the housing estate, giving your answer in km2.
Answers
Answer:
Given that:
A map is drawn to a scale of 1 : 25000.
(a) Two villages are 4.5km apart.
(b) A housing estate drawn on the map occupies an area of 40cm².
To Find:
(a) Their distance apart on the map in cm.
(b) The actual area of the housing estate, giving your answer in km².
(a) Converting the distance in cm.
1 km = 100000 cm
4.5 km = 450000 cm
Let us assume:
Their distance apart on the map be x.
According to the question.
↠ 1 : 25000 = x : 450000
↠ 1/25000 = x/450000
Cross multiplication.
↠ 450000 = 25000x
↠ 450000/25000 = x
↠ 18 = x
Hence,
(a) Their distance apart on the map is 18 cm.
(b) Converting the area in km².
1 cm² = 0.0000000001 km²
40 cm² = 0.000000004 km²
Let us assume:
The actual area of the housing estate be x.
According to the question.
↠ 1 : 25000 = 0.000000004 : x
↠ 1/25000 = 0.000000004/x
Cross multiplication.
↠ x = 0.000000004 × 25000
↠ x = 0.0001
Hence,
The actual area of the housing estate is 0.0001 km².
Step-by-step explanation:
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