A town planner is using a map of a town centre with a scale of 1 : 1250
The town planner wants to estimate the area of a plot of land. On the map it is 6cm ^2 . What is the corresponding area on the ground? Give your answer in square metres, rounded to 2 significant figures.
the real life area and the shape on the map are similar.
the ratio of similar shaped areas is equal to the squares of their corresponding dimensions.
so 1^2/1250^2 = 6/x
x=9375000 cm^2
= 937.5 m^2 (there are 10000 cm^2 in 1 m^2)
you were asked for 2 significant digits, so I would answer it as 940 m^2
could u ellaborate a little more on this please I cant quite grasp it
Of course, I'd be happy to elaborate further!
When dealing with maps and scales, it's important to understand the concept of similarity. In this case, the map and the actual land are similar in shape. This means that corresponding dimensions on the map and the ground have a proportional relationship.
To calculate the corresponding area on the ground, we need to use the ratio of similar shaped areas. The ratio of the areas is equal to the ratio of the squares of their corresponding dimensions. In other words, if the length on the map is L1 and the length on the ground is L2, then L1^2/L2^2 is equal to the ratio of the areas on the map and the ground.
In your specific problem, the area on the map is given as 6 cm^2. Let's call the corresponding area on the ground x m^2. Using the ratio of the areas, we have (1 cm)^2/(1250 cm)^2 = 6 cm^2/x. This is because the scale is 1:1250, meaning 1 cm on the map represents 1250 cm on the ground.
Simplifying the equation, we have 1/1250^2 = 6/x. To solve for x, we cross-multiply: 1 * x = 1250^2 * 6. Simplifying further, we get x = 9375000 cm^2.
However, the question asks for the answer in square meters. Since there are 10000 cm^2 in 1 m^2, we divide x by 10000 to convert it to square meters. Thus, the corresponding area on the ground is 937.5 m^2.
Finally, we round the answer to 2 significant figures as requested. In this case, the two significant figures are 93. Therefore, the final answer is 940 m^2.