What is a scale drawing?. http://www.basic-mathematics.com/scale-drawings.html. Scale Drawing. A drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount (called the scale).
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The scale is shown as the length in the drawing, then a colon (":"), then the matching length on the real thing.
Example: this drawing has a scale of "1:10", so anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.
Click on the Butterfly Below…
The scale indicates how many units of length of the actual object are represented by each unit of length in the drawing.
A scale of 1:1 implies that the drawing of the grasshopper is the same as the actual object.
The scale 2:1 suggests that the drawing is larger than the actual grasshopper -- twice as long and twice as high (we say the dimensions are multiplied by a scale factor of 2).
Island of the Little (48 s)
Island of the Giants (3min 33s)
A statement that shows two ratios are equivalent.
“The ratio of girls to boys in a class is 6:8 and there are 12 boys in the class.” A proportion can be set up and solved to find how many girls there are in the class.
_6_ = _X_
6 x 12 = 8 x X
72 = 8x
isolate the variable:
72 = 8x
X = 9 girls
By using proportions, you can find lengths needed to make a scale drawing or can find the actual lengths of an object based on a given scale drawing.
1 cm = 2.7cm
250 km X
x = 250 • 2.7 = 675 km.
2. ______ = 1 km
3. 1: 50,000
Example: Suppose a scale model has a scale of 2 inches = 16 inches. The scale factor is
2 or 1 16 8
The lengths and widths of objects of a scale drawing or model are proportional to the lengths and widths of the actual object.
In an illustration of a honey bee, the length of the bee is 4.8 cm. The actual size of the honeybee is 1.2 cm. What is the scale of the drawing?
4.8 cm = 1cm
1.2 cm x cm
4.8x = 1.2
x = .25
The scale of the drawing is 1 cm = .25cm
A set of landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4 feet.
What is the width of the actual flower bed?
Let x represent the actual width of the flower bed. Write and solve a proportion.
Plan width----> 1 inch = 6.5 inches<---plan width
Actual width--> 4 feet x feet <-----actual width
1x = 46.5 cross products
x= 26 The actual flower bed width is 26 feet.
To find the scale factor, write the ratio of 1 inch to 4 feet in simplest form.
1inch = 1 inch Convert 4 feet
4 feet 48 inches to inches
The scale factor is 1 . That is , each 48
measurement on the plan is 1 the actual measurement. 48
In a scale model of a roller coaster, the highest hill has a height of 6 inches. If the actual height of the hill is 210 feet, what is the scale of the model?
Model height---> 6 inches = 1 inch <--model height
Actual height--->210 feet x feet <--actual height
6x = 210
6x = 210x= 35
6 6 So, the scale is 1” =
On a set of architectural drawings for an office building, the scale is 1/2” = 3 feet. Find the actual length of each room.
Lobby: 2 inches
Cafeteria: 8.25 inches
.5” = 2”
3ft x ft
.5x = 6 The actual length
x = 12 of the lobby is 12 ft
.5” = 8,25”
3ft x ft The actual length of the
.5x = 24.75 cafeteria is 49.5 feet
x = 49.5
Place three or four objects on their desk.
Orient the objects parallel to the edges of the desk.
Use a 1:10 scale, with 1 cm on the map representing 10 cm of the desk top.
To help students appreciate what the scale is doing and how the numbers are used in calculating, the teacher may give students a 10 cm × 25 cm rectangle of paper to be one of the objects on the desk. This gives students one object for which it is easy to work out what the scaled version is; they may be able to generalize this to their other objects with more awkward dimensions. A second map using a different scale could then be produced, perhaps 2 cm = 5 cm (which is 1:2.5).
Graph paper may help students in drawing their maps.