Measurement: Rates, Scale and Similar Objects

Unit rates, scale diagrams and how a change in scale factor affects area, surface area and volume.

16 questions, free, marked as you go with a worked explanation on every one.

What this covers

The questions

  1. A car travels 450 km on 36 L of fuel. What is its fuel efficiency as a unit rate, in kilometres per litre?
  2. A scale model of a building is built at a scale of 1 : 50. A wall on the model measures 24 cm. What is the length of the real wall, in metres?
  3. Two similar triangles have a linear scale factor of 3. How do their areas compare?
  4. A cube has a volume of 40 cm³. Every edge is then doubled in length. What is the volume of the enlarged cube, in cubic centimetres?
  5. A printer produces 130 pages in 4 minutes at a steady rate. A school needs 1 950 pages printed for an exam. How many minutes will the printer take?
  6. On a map with a scale of 1 : 25 000, two towns are 8.4 cm apart. What is the actual distance between them, in kilometres?
  7. On a graph of distance against time for a vehicle moving at a steady speed, what does the slope of the line represent?
  8. Two similar cylindrical tanks have heights of 2 m and 5 m. The smaller tank holds 16 000 L. How many litres does the larger tank hold?
  9. A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm. What is its volume, in cubic centimetres?
  10. A cylindrical water tank has a radius of 0.5 m and a height of 2 m. Using V = pi times r squared times h, and pi approximately 3.14, what is its volume, in cubic metres, rounded to two decimal places?
  11. A cube is enlarged by doubling each edge. By what factor does its volume increase?
  12. A cone has a radius of 3 cm and a height of 7 cm. Using V = one third times pi times r squared times h, and pi approximately 3.14, what is its volume in cubic centimetres, rounded to the nearest whole number?
  13. A line passes through the points (2, 5) and (6, 13). What is its slope?
  14. A line has a slope of 0. What does this tell you about the line?
  15. A ramp rises 2.5 m over a horizontal run of 10 m. What is its slope, as a decimal?
  16. On a graph of cost against number of items bought, what does the slope of the line represent?

Answer these free