Nuffield Free-Standing Mathematics Activity Hot water tank Formulae

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

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

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

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

Example Area of a circle with radius 5 cm A = r 2 = 5 2 5 cm = 78. 5398. . . Think about… How far should this be rounded? Area = 79 cm 2 (nearest cm 2) Example Volume of a sphere with radius 5 cm V = 4 r 3 = 4 53 3 3 V = 523. 5987. . . Think about… How do you work this out on a calculator? Volume = 524 cm 3 (nearest cm 3)

Example Area of a trapezium with height 4. 8 cm and parallel sides of length 4. 3 cm and 6. 4 cm h (a + b) A= 2 = a = 4. 3 height h = 4. 8 (4. 3 + 6. 4) 2 Think about… What ways could be used to work this out? Area = 25. 68 = 26 cm 2 (nearest cm 2) b = 6. 4

Example Surface area of a cylindrical tank with radius 1. 6 m and height 2. 7 m S = 2 r (r + h) radius r height h = 2 1. 6 (1. 6 + 2. 7) Think about… What ways could you use to work this out? Surface area = 43. 228. . . Think about… How far should this be rounded? = 43 m 2 (to nearest m 2)

Example £P left in building society at r % interest. Amount after n years: A = P (1 + 100 )n r If £ 750 is invested at 4. 5 % interest for 6 years: A = 750 (1 + 4. 5 )6 100 Think about… How do you work this out? = 750 1. 0456 = 976. 695. . . Think about… How far should this be rounded? Amount = £ 976. 70 (nearest pence)

Example Radius of sphere r= where V is the volume. 3 3 V 4 The radius of a ball bearing whose volume is 9. 6 mm 3 r= 3 3 x 9. 6 4 Think about… How do you work this out on a calculator? = 3 2. 29183. . . = 1. 318… Radius = 1. 3 mm (to 2 sf) Think about… Can you think of other examples where you have met formulae before?

Hot water tank: Formulae 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? When working out the value of a formula, how do you decide in what order to press the calculator buttons? Were there any examples where you found it difficult to use the calculator correctly? Which did you find the most complicated?