Ratios
Mathematics Worked Examples by Topics
| Number | Mathematical Skills | Applications |
|---|---|---|
| 1 | Number, percentages, and percentiles | Determining the amounts, costs, and dimensions of materials |
| 2 | Ratio | Scaling models, dimensions, shapes, and drawings |
| 3 | Surface area/Volume | Finding costs of quantities, waste amounts |
| 4 | Trigonometry | Calculating angles/lengths of products |
| 5 | Graphs and charts | Using data to make decisions/visualization of data |
| 6 | Coordinates and geometry | Using coordinates for design drawings |
| 7 | Statistics | Using data to make informed design decisions |
Ratio
Question 1)
A kayak manufactuer is using epoxy adhesive to bond the fibre glass layers together in the kayak design.
- The kayak will require 5.3m2 of fibreglass
- 5 litres of Epoxy adhesive is needed per metre squared
- The ratio of resin to hardener for the epoxy adhesive is 3:4
Calculate the volume of hardener needed for 100 kayaks.
Step 1) Calculate the amount of epoxy adhesive needed for 1 kayak:
Epoxy resin needed = 5.3 x 5 = 26.5 litresStep 2) Calculate the amount of hardener needed:
Hardener needed = 4⁄7 x 26.5 = 15.14 litresStep 3) Calculate the volume needed for 100 kayaks:
Total volume = 15.14 x 100 = 1514 litresQuestion 2)
A games console developer has designed a new plastic controller. The controller must have a free space interior volume of 250cm3 for electrical components.
- The occupied space in the controller is 180cm3
- The ratio of occupied space to free space is 4:5
Is there enough space in the controller for the electronics. Show your working.
Step 1) Calculate the amount of volume '1 ratio part' is equivalent to:
1 ratio part = 180⁄4= 45Step 2) Calculate the amount of free space using the ratio:
Free space = 45 x 5 (5 ratio parts free space) = 225cm3225 is smaller than 250, not enough free space
Question 3)
A student needs to cut a plank of wood into three pieces in the ratio 2:5:9. The plank is 360cm. Calculate the longest piece.
Step 1) Calculate the total 'ratio parts':
Total 'ratio parts' = 2 + 5 + 9 = 16Step 2) Calculate the length of one 'ratio part':
1 ratio part = 360⁄16 = 22.5Step 2) Calculate the longest length (9 'ratio parts'):
Longest length = 22.5cm x 9 = 202.5cm