# Worksheet: Solving Problems Involving Scale Drawings

Q1:

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

• A
• B
• C
• D

Q2:

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

• A
• B
• C
• D
• E

Q3:

If the distance between two cities on a map is 13.5 cm and the map has a drawing scale of , determine the actual distance between the cities.

Q4:

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

• A
• B
• C
• D
• E

Q5:

Determine the scale factor for .

• A
• B
• C
• D
• E

Q6:

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

Q7:

Determine the actual length and width of the given rectangle which is drawn to a scale of 1 in = 2 ft.

• Alength = 3 ft, width = 1 ft
• Blength = 6 ft, width = 3 ft
• Clength = 12 ft, width = 6 ft
• Dlength = 6 in, width = 3 in
• Elength = 12 in, width = 6 in

Q8:

Find the scale factor used to dilate square to square .

• A2
• B
• C
• D
• E

Q9:

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

Q10:

A picture of a tower is taken with a drawing scale of . If the height of the tower in the picture is 6 cm, what is its real height?

• A3 m
• B294 m
• C18 m
• D1 m
• E50 m

Q11:

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.

Q12:

A square-shaped piece of land has a perimeter of 672 m. If you use a scale of to make a drawing of the land, how long would each side of the drawing be in centimetres?

Q13:

Russell made a drawing of his brother Christopher with a drawing scale of . If Christopher’s height is 135 cm, what is his height in the drawing?

• A15 cm
• B13 cm
• C9 cm
• D90 m
• E120 cm

Q14:

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

• A
• B
• C
• D
• E

Q15:

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

Q16:

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

Q17:

The figure below represents the floor plan of a house, where the drawing scale is . What is the real-life area of the living room?

Q18:

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