Question

A roof area of 6000 m\(^2\) of a building is drafted on a drawing sheet as 240 cm\(^2\). The scale used in the drawing sheet is 1:__________ (rounded off to the nearest integer)

Hint:

When calculating scale ratios, remember that the area ratio needs to be converted into a linear scale by taking the square root of the area ratio.

Answer 1

The drawing's scale is defined as the ratio of the real-world area to the area depicted on the drawing.

Step 1: The actual roof area is \( 6000 \, \text{m}^2 \), and its representation on the drawing is \( 240 \, \text{cm}^2 \).

Step 2: Convert the actual area to square centimeters: \[ 6000 \, \text{m}^2 = 6000 \times 10^4 = 60,000,000 \, \text{cm}^2 \]

Step 3: The scale is calculated by dividing the actual area by the area on the drawing: \[ \text{Scale} = \frac{\text{Actual area}}{\text{Area on drawing}} = \frac{60,000,000 \, \text{cm}^2}{240 \, \text{cm}^2} = 250,000 \] To express the scale as 1:n, the square root of this ratio is taken: \[ \sqrt{250,000} = 500 \]

Conclusion: The drawing utilizes a scale of 1:500.