Worksheet: Scale Drawings and Models

In this worksheet, we will practice calculating the scale factor for any scaled drawing, the length of the scaled object in the drawing, or its length in reality and using this to solve problems in a real-world context.

Q1:

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

Q2:

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

Q3:

Determine the scale factor for .

Q4:

Determine the scale factor for the following: 1 inch feet.

Q5:

The radii of two circles are 12 cm and 4 cm. Find the scale factor of the first circle to the second.

Q6:

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

Q7:

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?

A1 inch feet
B1 inch feet
C1 inch feet
D1 inch feet
E1 inch feet

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.

A1 inch feet
B1 inch feet
C1 inch feet
D1 inch feet
E1 inch feet

Q9:

An engineer makes a model of 600 metre tall tower to a scale of . What is the model’s height in centimetres?

Q10:

The scale factor of a model of a human inner ear to the actual ear is . If one of the bones of the model is 11 centimeters long, determine, to the nearest hundredth, the length of the actual bone in a human ear.

Q11:

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.

Q12:

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.

Q13:

A map is scaled such that every 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:

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

Q16:

A model of a tree is made using a scale of . Find the height of the actual tree if the height of the model is in.

A30 ft
B80 ft
C ft
D ft

Q17:

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 ft
B ft
C ft
D46 ft
E ft

Q18:

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

Q19:

Arthur 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.

Q20:

Determine the actual area of the given square which is drawn to a scale of 15 cm = 4 km.

Q21:

Using the shown scale drawing of a room, determine its actual length if its actual width is 36 feet.

Q22:

In the following plan of an apartment, each square has a side length of in, and the scale is . Find the actual width and length of the kitchen.

A ft wide, 15 ft long
B90 ft wide, 150 ft long
C ft wide, ft long
D ft wide, ft long
E15 ft wide, ft long