Creating or interpreting drawings and models where every length is multiplied by the same constant (the scale factor), preserving shape while changing size.
A map is a scale drawing of the real world. If 1 inch on the map equals 10 miles in reality, the scale factor is 1:10 miles. Every distance on the map uses the same ratio, so the shapes stay accurate—just smaller. Enlarging a photo works the same way in reverse.
Showing a random 20 of 50 problems.
Example 1
challenge
A 1:25 model of a swimming pool holds 32 L of water. The real pool's owner wants to know how many cubic meters fill it.
Example 2
easy
On a 1:100 blueprint, a door is drawn 2 cm tall. The real door is ___ cm tall.
Example 3
medium
An architect's drawing has scale 21 inch=1 foot. A wall is drawn 7 inches long. How long is the real wall?
Example 4
easy
A drawing uses scale 2 cm : 5 m. A wall is 20 m long. How long is it in the drawing?
Example 5
hard
Two similar triangles have areas 32 and 50. Find the ratio of their corresponding sides.
Example 6
hard
A lake covers 3.2 km2 in reality and 20 cm2 on a map. Find the linear scale 1:n.
Example 7
medium
A blueprint scale is 1/4 inch = 1 foot. A wall is 18 feet. How long on the blueprint?
Example 8
medium
A scale drawing has scale 1:25. The real area of a plot is 625 m2. What is the drawing's area in cm2?
Example 9
easy
A model car is built at a scale of 1:24. The model car is 15 cm long. How long is the actual car in meters?Model car at 1:24 scale — find the real length (answer: 3.6 m)
Example 10
medium
A 1:10 model holds 2 L of water. How much does the real object hold (volume scaling)?
Example 11
challenge
A map is at scale 1:n. A lake covers 8 cm² on the map and 2 km² in reality. Find n.
Example 12
medium
Two similar maps: one at 1:50000, another at 1:25000. The same road is 4 cm on the first map. How long is it on the second?
Example 13
easy
A scale 1:200 means the drawing is ___ of the real size.
Example 14
easy
A map scale is 1:50,000. Two landmarks are 4 cm apart. How far apart are they in km?
Example 15
medium
A floor plan at scale 1:40 shows a room 5 cm ×8 cm. Find the room's real area in m2.
Example 16
easy
Scaling lengths by factor k=3 multiplies the area by what factor?
Example 17
medium
A 1:20 model boat holds 0.5 L of water. How much does the real boat hold (assuming volume scaling)?
Example 18
challenge
Why can't a giant ant the size of a car exist, in terms of scaling of strength vs weight?
Example 19
challenge
Two similar triangles have areas 18 and 50. Find the ratio of their corresponding sides.
Example 20
challenge
An architect draws a 30 m tall tower on A4 paper that is 29.7 cm tall, allowing 3 cm of margin at the top and bottom. What is the largest sensible scale 1:n (smallest n) usable, with n a round multiple of 50?