Chapter 12. Mathematics and Science for Technicians
Units. Use the metric (SI) system: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K). Common conversions: 1 m = 1,000 mm = 100 cm; 1 kg = 1,000 g; 1 L = 1,000 mL; 1 hour = 3,600 s. Always include units in calculations.
Basic formulas
| Quantity | Formula |
| Rectangle area | length × width |
| Triangle area | ½ × base × height |
| Circle area | πr² |
| Circumference | 2πr |
| Volume of a box | length × width × height |
| Volume of a cylinder | πr²h |
| Speed | distance / time |
| Density | mass / volume |
| Pythagoras (right triangle) | a² + b² = c² |
Percentages and ratios. Percent of a quantity = (percent / 100) × quantity. Ratios and proportions are used for mixing concrete, paint and fluids, and for scaling drawings.
Squaring a corner. The 3-4-5 triangle: if the sides are 3, 4 and 5 units, the angle between the 3 and 4 sides is a right angle. Builders use this check on site [9][16].
Formulas and rearranging. To find an unknown, rearrange the formula: from V = IR, I = V/R and R = V/I.
Estimating and checking. Estimate an answer first, calculate carefully, then judge whether the result is reasonable. Keep calculations neat so they can be checked.
Science links. Basic physics (force, energy, pressure, heat, electricity) and chemistry (corrosion, combustion, fuels, adhesives) underpin most trades [8][11].
Review: Find the volume of a cylinder with radius 0.1 m and height 0.5 m. (Answer: π × 0.01 × 0.5 ≈ 0.0157 m³, or about 15.7 litres.)