1) on a map of scale 1cm to 250m the area of car park is 3cm^2.what is the actual area of the car park in hecares(1 hectare= 10,000m^2)
2)The area of the playing surface at wembly stadium is 3/5 of a hectare . what area willit occupy on a plan drawn to a scale of 1:500?
1) Well, let's do some math, shall we? If 1cm on the map represents 250m, then 1cm^2 would represent 250m * 250m, which is 62,500m^2. But hang on, the car park on the map is only 3cm^2, so we need to multiply 62,500m^2 by 3. That gives us a car park size of 187,500m^2. Phew!
So, the actual area of the car park in hectares would be 187,500m^2 divided by 10,000m^2/hectare, which gives us 18.75 hectares. That's quite a spacious car park, huh?
2) Ah, Wembley Stadium, the home of grand football matches and epic concerts! So, if the playing surface area is 3/5 of a hectare, we need to figure out its size on a 1:500 scale plan.
If 1cm on the plan represents 500m, then 1cm^2 would represent 500m * 500m, which is 250,000m^2. Now, we need to calculate 3/5 of a hectare in square meters, which is (3/5) * 10,000m^2, giving us 6,000m^2.
So, to find the area on the plan, we divide 6,000m^2 by 250,000m^2/cm^2 to get 0.024cm^2. Therefore, the playing surface would occupy an area of 0.024cm^2 on the plan. It might sound tiny, but trust me, it's massive when you're standing there on the actual field!
1) To find the actual area of the car park in hectares, we need to use the given scale and relate it to the actual measurements.
The given scale is 1cm to 250m. This means that every 1cm on the map represents an actual distance of 250m.
The area of the car park on the map is given as 3cm^2. We can find the actual area by multiplying this by the scale factor.
Area on map = 3cm^2
Scale factor = 250m/1cm = 250
Actual area = Area on map x Scale factor
= 3cm^2 x 250m/1cm
= 3 x 250 m^2
= 750 m^2
To convert the actual area from square meters to hectares, we divide by 10,000 square meters in a hectare.
Actual area in hectares = 750 m^2 / 10,000m^2/ha
= 0.075 hectares
Therefore, the actual area of the car park is 0.075 hectares.
2) The area of the playing surface at Wembley stadium is given as 3/5 of a hectare.
To find the area it will occupy on a plan drawn to a scale of 1:500, we need to use the scale factor.
The scale is 1:500, which means that every 1 unit on the plan represents 500 units in actual measurements.
Given area = 3/5 hectare
To find the area on the plan, we multiply the given area by the scale factor squared.
Area on plan = Given area x (Scale factor)^2
= (3/5 hectare) x (500)^2
= (3/5) x 500^2 hectare
= (3/5) x 250,000 hectare
= 150,000/5 hectare
= 30,000 hectares
Therefore, the area of the playing surface at Wembley stadium on the plan drawn to a scale of 1:500 is 30,000 hectares.
To answer both of these questions, we'll need to use the concept of scale. Scale is a representation of the relationship between the measurements on a map or plan and the actual measurements of the real object or area. In other words, it allows us to determine the real-world measurements based on the scaled representation.
1) The scale of the map is given as 1cm to 250m. This means that for every 1cm on the map, it represents an actual distance of 250m. We are given that the area of the car park on the map is 3 cm^2.
To find the actual area of the car park in hectares, we need to convert the scaled area to the actual area using the scale.
First, we need to convert the scaled area from cm^2 to m^2. Since 1cm on the map represents 250m, we can square the scale factor (250) to get the conversion factor for the area.
Conversion factor = (250m)^2 = 62,500m^2/cm^2
Now, to convert the scaled area of 3cm^2 to m^2, we multiply it by the conversion factor:
Actual area = 3cm^2 * 62,500m^2/cm^2 = 187,500m^2
Finally, to convert the area from square meters to hectares, we divide by the conversion factor for hectares:
Actual area in hectares = 187,500m^2 / 10,000m^2/hectare = 18.75 hectares
2) In this question, we are given that the area of the playing surface at Wembley Stadium is 3/5 of a hectare. We need to find the area it would occupy on a plan drawn to a scale of 1:500.
Since the scale is given as 1:500, this means that for every 1 unit on the plan, it represents 500 units in the real world.
To find the area on the plan, we need to first convert the area from hectares to square meters using the conversion factor for hectares:
Area in square meters = (3/5 hectare) * (10,000m^2/hectare) = 6,000m^2
Now, we divide the area in square meters by the square of the scale factor (500)^2 to get the area on the plan:
Area on the plan = 6,000m^2 / (500)^2 = 0.24m^2
Therefore, the area of the playing surface on the plan drawn to a scale of 1:500 would be 0.24 square meters.
123
1. Ratio=1cm/250m = 1cm/25000cm = 1/25000.
A=25,000 * 3cm^2 = 75,000cm^2 = 7.5m^2.
A=7.5m^2/10000m^2/hec=0.00075hectares
2. A = (3/5)10,000m^2 = 6000m^2.
A = 6000m^2 / 500 = 12m^2 on a drawing,