Worksheet: Scale Drawings and Models

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In this worksheet, we will practice calculating the scale factor and the lengths of both the scaled model and the actual one and applying this to real-world problems.

Q1:

The distance between two cities on a map is 17 cm and the actual distance between them is 68 km. If the distance between two other cities on the same map is 15 cm, determine the real distance between them.

Q2:

A line on a drawing is 3 cm long. In real life, the object represented is 5 7 km long. What is the drawing scale?

  • A 1 : 5,700,000
  • B 1 : 1,900,000
  • C 1 : 57,000
  • D 1 : 190,000
  • E 1 : 300

Q3:

William is drawing a map to a scale of 1 ∶ 1 0 0 0 0 0 0 0 . If the distance between two cities on the map is 4.5 cm, find the actual distance between them in kilometers.

Q4:

A model of a tree is made using a scale of 1 ∶ 3 0 i n f t . Find the height of the actual tree if the height of the model is 2 2 3 in.

  • A 30 ft
  • B 80 ft
  • C 2 2 3 ft
  • D 4 4 5 ft

Q5:

A picture with width 13 mm and height 37 mm is magnified so that its width becomes 3.25 cm and height becomes 𝑋 cm. Find the value of 𝑋 .

Q6:

An engineer makes a model of 600-meter-tall tower to a scale of 1 7 5 0 : . What is the model’s height in centimeters ?

Q7:

Determine the scale factor for 3 = 2 . 7 c m m .

  • A 1 9 :
  • B 1 2 . 7 :
  • C 1 3 :
  • D 1 2 7 :
  • E 1 9 0 :

Q8:

An apartment’s ceiling is 19 feet high. However, its height on a scale drawing is only 4 inches. Determine the scale of the drawing.

  • A 1 inch = 57 feet
  • B 1 inch = 14.25 feet
  • C 1 inch = 2.53 feet
  • D 1 inch = 0.21 feet
  • E 1 inch = 4.75 feet

Q9:

If the scale factor from a statue to a reduced model for a display is 16 feet to 7 feet, and the height of the original statue is 55 feet, find the height of the model.

  • A 3 7 1 6 ft
  • B 2 2 5 5 ft
  • C 2 4 1 1 6 ft
  • D 46 ft
  • E 7 6 7 ft

Q10:

Given a scale drawing, which of the following is equal to the scale?

  • A l e n g t h i n r e a l i t y l e n g t h i n d r a w i n g
  • B l e n g t h i n d r a w i n g l e n g t h i n r e a l i t y
  • C l e n g t h i n d r a w i n g l e n g t h i n r e a l i t y +
  • D l e n g t h i n d r a w i n g l e n g t h i n r e a l i t y ×

Q11:

At a scary movie opening, a cardboard model of the monster was 9 inches tall. In the movie, the monster’s actual height was 53 feet. What was the scale of the model?

  • A 1 = 9 5 3 i n c h f e e t
  • B 1 = 5 8 9 i n c h f e e t
  • C 1 = 7 0 2 3 i n c h f e e t
  • D 1 = 1 7 2 3 i n c h f e e t
  • E 1 = 2 2 5 3 i n c h f e e t

Q12:

A scale model of a building is 4.8 inches tall. If 2 inches on the model scale up to 25 feet in reality, determine the actual height of the building.

Q13:

A map is scaled such that every 1 8 in is equivalent to 50 mi. How many miles are represented by 4 inches on the map?

Q14:

An insect’s body is 9 centimeters long with 21-centimeter legs. Determine the length of its legs in a model where its body is 3 meters long.

Q15:

Jacob drew a map of his school using a scale of 1 inch for every 10 ft. Determine the distance with which the 800 feet between the playground and the boys restroom would be represented on the map.

Q16:

Determine the actual area of the given square which is drawn to a scale of 1 cm = 4 km.

Q17:

Given that the distance between two cities on a map is 4.4 cm and the actual distance between them is 26.4 km, what is the drawing scale of the map?

  • A 1 ∶ 6 0 0 , 0 0 0
  • B 1 ∶ 6 0 , 0 0 0
  • C 1 ∶ 4 , 0 0 0
  • D 1 ∶ 2 4 , 0 0 0
  • E 1 ∶ 1 0 5 , 6 0 0

Q18:

Complete the table.

Drawing Distance Real Distance Scale Magnification or Reduction
4.2 dm 30 km … …
  • A 7 5 0 , 0 0 0 : , reduction
  • B 5 0 , 0 0 0 7 : , magnification
  • C 7 5 0 0 , 0 0 0 : , reduction
  • D 5 0 0 , 0 0 0 7 : , magnification

Q19:

Complete the table.

Drawing Distance Real Distance Scale Magnification or Reduction
cm 90 km 7 ∶ 9 0 0 , 0 0 0
  • A70, magnification
  • B7, reduction
  • C7, magnification
  • D70, reduction

Q20:

The figure below shows a drawing of the floor plan of a house. The drawing scale is 1 ∶ 1 0 0 . What is the length and width of the real-life living room?

  • A 6.4 m, 3.6 m
  • B 12.8 m, 7.2 m
  • C 16 m, 9 m
  • D 64 m, 36 m

Q21:

The table below shows some information about a scale drawing. Complete the missing details, including whether the drawing is a magnification or reduction from real life.

The Drawing Distance The Real Distance The Scale Magnification or Reduction
66 cm mm 2 2 ∶ 1
  • A30, magnification
  • B30, reduction
  • C1, reduction
  • D1, magnification
  • E3, magnification

Q22:

A map is drawn with a drawing scale of 1 ∶ 3 , 8 0 0 , 0 0 0 . If the actual distance between two cities is 76 km, determine the distance between them on the map.

Q23:

A rectangular picture with width 20 mm and height 61 mm is magnified to 4 cm by 12.2 cm. What is the magnification ratio?

  • A 2 1 :
  • B 2 0 1 :
  • C 2 0 6 1 :
  • D 4 0 6 1 :

Q24:

Every inch in a scale model of a car represents 1 2 ft in reality. If a vehicle is 4 1 2 ft long, how long is the scale model?

  • A 9 in
  • B 4 1 2 in
  • C 1 2 in
  • D 2 1 4 in

Q25:

Find the scale factor of the smaller parallelogram to the bigger one in the given figure.

  • A2
  • B 1 3
  • C3
  • D 2 3
  • E 1 2

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