road measuring 400 km was drawn to the scale f \( 1: 10000000 \). Determine the drawing length f the road in centimetres.

To determine the drawing length of a 400 km road at a scale of 1:10,000,000, you first convert the actual length from kilometers to centimeters. Since 1 km is equivalent to 100,000 cm, then 400 km becomes 400 x 100,000 = 40,000,000 cm. Now, applying the scale, divide the actual length in cm by the scale factor: 40,000,000 cm / 10,000,000 = 4 cm. Thus, the drawing length of the road is 4 cm. Real-world application of scale drawings is prevalent in various fields such as architecture and engineering, where precise representations of large structures or distances need to be effectively communicated on paper. For example, when planning a new highway or building, architects use a scale to create accurate blueprints, ensuring they can visualize how the finished project will fit within its intended space before construction begins. Common mistakes when working with scale drawings include forgetting to consistently apply the scale factor throughout the drawing process, which can lead to inaccuracies in representation. It's also crucial to double-check your conversions; a simple miss in units can turn a flawless design into a perplexing problem later on. Always remember to keep your working notes organized and label your scales clearly to avoid any mix-ups!