11+ Maths Solved Topic Wise Questions

1. Scale Drawings

Scale drawings form a crucial part of everyday life. Scale drawings are useful in a variety of careers from town planning to architecture. Buildings, houses and even cars have all been constructed by following a scale drawing. 

Scale drawings represent smaller form of the real area or object. A scale is used to compare. For example, scale of 1 mm = 5 m means 1 mm on map or drawing is the same as 5 m in real life. In ratio form, for example, the scale is given as 1 : 300, which means 1 cm on map or drawing is 300 cm in real life. 

1.1 Why do we need Scale Drawings

Take for example constructing a building or manufacturing a car, it is not possible to draw the real size of the building or a car on a paper or a map. We need scale drawings which to represent the plan and map of the  building or the car which can be drawn on the actual paper size. 

Let us look at the truck below.

The length of this truck is nearly 60 feet or 720 inches. However the length of the actual paper size which you might use to draw this truck is a little bit less than 12 inches. Since 720/12 = 60, you will need 60 sheets of actual paper size to draw the length of the actual size of  the  truck.

So we use scale drawing to draw the same truck using smaller measurements. In order to draw this truck in one paper, you could use 1 inch of your drawing to represent 60 inches on the  real life object.

You can write the scale as 1:60 or 1/60 or 1 to 60.

1.2 Solved Examples

Example: Simplify the scale of 2 cm : 5 km

Solution: Using relations 1m = 100 cm and 1 km = 1000 m,

               2 cm : 5 km = 2 cm : 5000 m

                                   = 2 cm : 500000 cm

                                   = 2 : 500000

                                   = 1 : 250000

Example: A particular map shows a scale of 1 cm = 8 km. What would the map distance be (in cm) if the actual distance is 24 km?

Solution: Scale is 1 cm : 8 km

               So the map distance : actual distance = 1 cm : 8 km

               Actual distance is 24 km

               Let the map distance be x cm.

               1 cm ÷ 8 km = x cm ÷ 24 km

                x = 24 × 1 ÷ 18

                x = 3 cm

                The map distance would be 3 cm.