(a) A street guide for Belfast has a scale of 1:15 000. A walkway through the city is 2.4 km long. Find the length of the walkway on the map. Give your answer in centimetres.
(b) Ormeau Park in Belfast has an area of about 25 cm2 on the same map. Calculate the area of the park on the ground. Give your answer in km2, correct to 2 significant figures
To solve these questions, we need to use the scale provided (1:15 000) to convert the measurements from the map to real-world measurements.
(a) To find the length of the walkway on the map in centimeters, we need to convert the real-world distance (2.4 km) into the corresponding distance on the map.
Step 1: Convert kilometers to centimeters using the scale.
1 kilometer = 100,000 centimeters (since there are 1000 meters in a kilometer and 1 meter = 100 centimeters)
Step 2: Use the scale of 1:15,000 to convert centimeters on the map.
1 centimeter on the map represents 15,000 centimeters in reality.
Therefore:
Length on the map (in centimeters) = (2.4 km * 100,000 cm/km) / 15,000
= (240,000 cm) / 15,000
= 16 cm
So, the length of the walkway on the map is 16 centimeters.
(b) To calculate the area of Ormeau Park on the ground in square kilometers, we need to convert the area on the map (25 cm²) to real-world units.
Step 1: Use the scale of 1:15,000 to convert square centimeters on the map.
1 square centimeter on the map represents (15,000 * 15,000) square centimeters in reality.
Step 2: Convert square centimeters to square kilometers.
1 square kilometer = 10^10 square centimeters (since there are 100,000 centimeters in a kilometer)
Therefore:
Area on the ground (in square kilometers) = (25 cm² * (15,000 * 15,000 cm²/1 cm²)) / (10^10 cm²/km²)
= (25 * 15,000 * 15,000) / (10^10)
= 5.625 km² (rounded to 2 significant figures)
So, the area of Ormeau Park on the ground is approximately 5.63 km².