Answer:
a. 1 200 000 km
b. 0.000 773 cm
c. 67 500 000 000 km²
d. 0.000 000 016 cm²
Step-by-step explanation:
a. Calculate the ACTUAL distance, in km, between two places which are 16 cm apart on the map.
Since the scale is 1 : 75000 that is 1 cm : 75000 km, we want to find the actual distance of 16 cm on the map. Let x be the actual distance in km.
So, 1 cm : 75000 km = 16 cm : x km
So, 1 cm/75000 km = 16 cm/x km
Thus x km = 16 cm × 75000 km/1 cm = 1 200 000 km
(b) Calculate length of a road on the map which is 0.58 km.
Let y be the length of road on the map. So, using our scale
1 cm : 75000 km = y cm : 0.58 km
So, 1 cm/75000 km = y cm/0.58 km
Thus y cm = 0.58 km × 1 cm/75000 km = 0.000 773 cm
(c) Calculate, in km², the ACTUAL area of a lake which is 12 cm2 on the map.
Since the scale is 1 : 75000 , the scale for the area would be the square of this. So, 1² : 75000² = 1 : 5 625 000 000 which is 1 cm² : 5 625 000 000 km²
Let z be the actual area of the lake.
So, 1 cm² : 5 625 000 000 km² = 12 cm² : z km²
So, 1 cm²/5 625 000 000 km² = 12 cm²/z km²
Thus z km² = 12 cm² × 5 625 000 000 km²/1 cm² = 67 500 000 000 km²
(d) Calculate the area of a play field on the map which has has an actual area of 90 km².
Let a represent the area of the play field on the map. Using our scale for the area,
1 cm² : 5 625 000 000 km² = a cm² : 90 km²
So, a cm² = 90 km² × 1/5 625 000 000 km² = 0.000 000 016 cm²
× 100
= -0.25 × 100 = -25