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 scale of the drawing is given as the ratio of the actual area to the area on the drawing sheet.

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

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

Step 3: The scale is the ratio of the actual area to the area on the drawing sheet: \[ \text{Scale} = \frac{\text{Actual area}}{\text{Area on drawing}} = \frac{60,000,000 \, \text{cm}^2}{240 \, \text{cm}^2} = 250,000 \] To get the scale in terms of 1:n, we take the square root of the ratio: \[ \sqrt{250,000} = 500 \]

Conclusion: The scale used in the drawing sheet is 1:500.