1. © Nuffield Foundation 2011 Nuffield Free-Standing Mathematics Activity Hot water tank: Formulae

2. These solar panels provide hot water for a house. V =  r 2 h Think about… What do the letters represent in this formula? Formulae How can you work out how much hot water the tank will hold? To do this you need to use a formula

3. Variables are values that are not fixed. Fixed values such as the number of days in a week, 7, are called constants.  is a constant. In algebra letters are used to represent numbers. Formulae are used to give the relationship between variables. Some formulae also involve constants. Formulae

4. How to work out the volume of the tank… V =  r 2 h V =   30  30  150 = 424 115 cm 3 1000 cm 3 = 1 litre Volume = 424 litres (nearest litre) Think about… Is this a sensible way to give the answer? Think about… Is this a reasonable answer? How many baths is it? (A bath holds about 80 litres.) diameter 60cm height 150cm

5. A =  r 2 Example Area of a circle with radius 5 cm 5 cm =   5 2 = 78.5398... Area = 79 cm 2 (nearest cm 2 ) Example Volume of a sphere with radius 5 cm V = 523.5987... Volume = 524 cm 3 (nearest cm 3 ) V =  r 3 4 3 =   5 3 4 3 Think about… How far should this be rounded? Think about… How do you work this out on a calculator?

6. A = h (a + b) 2 Example Area of a trapezium with height 4.8 cm and parallel sides of length 4.3 cm and 6.4 cm height h = 4.8 b = 6.4 a = 4.3 = 4.8 (4.3 + 6.4) 2 = 26 cm 2 (nearest cm 2 ) Area = 25.68 Think about… What ways could be used to work this out?

7. S = 2  r ( r + h ) radius r height h Example Surface area of a cylindrical tank with radius 1.6 m and height 2.7 m = 2   1.6 (1.6 + 2.7) = 43 m 2 (to nearest m 2 ) Surface area = 43.228... Think about… How far should this be rounded? Think about… What ways could you use to work this out?

8. £ P left in building society at r % interest. Amount after n years: Example r 100 A = P (1 + ) n A = 750 (1 + ) 6 100 4.5 If £750 is invested at 4.5 % interest for 6 years: = 750  1.045 6 = 976.695... Amount = £976.70 (nearest pence) Think about… How do you work this out? Think about… How far should this be rounded?

9. The radius of a ball bearing whose volume is 9.6 mm 3 Radius of sphere where V is the volume. Example r = 3V3V 44 3 3 x 9.6 44 3 = 2.29183... 3 Radius = 1.3 mm (to 2 sf) = 1.318… Think about… How do you work this out on a calculator? Think about… Can you think of other examples where you have met formulae before?

10. At the end of the activity The formula for the volume of a tank is V =  r 2 h Which of the letters are variables and which is a constant? Were there any examples where you found it difficult to use the calculator correctly? Which did you find the most complicated? Hot water tank: Formulae When working out the value of a formula, how do you decide in what order to press the calculator buttons?