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# Nuffield Free-Standing Mathematics Activity Hot water tank: Formulae

Nuffield Free-Standing Mathematics Activity Hot water tank: Formulae. 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.

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## Nuffield Free-Standing Mathematics Activity Hot water tank: Formulae

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

2. 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 =  r2h Think about…What do the letters represent in this formula?

3. 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. Variablesare values that are not fixed. Formulae are used to give the relationship between variables. Some formulae also involve constants.

4. How to work out the volume of the tank… diameter 60cm V =  r2h V =  30  30  150 = 424 115 cm3 height150cm Think about…Is this a sensible way to give the answer? 1000 cm3 = 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.)

5. 5 cm V =  r3 4 4 3 3 Example Area of a circle with radius 5 cm A = r2 = 52 = 78.5398... Think about…How far should this be rounded? Area = 79 cm2 (nearest cm2) Example Volume of a sphere with radius 5 cm Think about…How do you work this out on a calculator? = p53 V = 523.5987... Volume = 524 cm3 (nearest cm3)

6. a= 4.3 h (a + b) height h= 4.8 A = 2 b= 6.4 4.8(4.3+6.4) = 2 ExampleArea of a trapezium with height 4.8 cm and parallel sides of length 4.3 cm and 6.4 cm Think about…What ways could be used to work this out? = 26 cm2 (nearest cm2) Area = 25.68

7. radius r heighth Example Surface area of a cylindrical tank with radius 1.6 m and height 2.7 m S = 2 r(r+h) = 21.6(1.6+2.7) Think about…What ways could you use to work this out? Think about…How far should this be rounded? Surface area = 43.228... = 43 m2 (to nearest m2)

8. Example £P left in building society at r% interest. Amount after n years: A = P (1 + )n 4.5 100 A = 750 (1 + )6 100 r If £750 is invested at 4.5% interest for 6 years: Think about…How do you work this out? = 750  1.0456 Think about…How far should this be rounded? = 976.695... Amount = £976.70 (nearest pence)

9. Example Radius of sphere where V is the volume. 3V 3 r = 4 3 3 x 9.6 3 2.29183... r = = 4 The radius of a ball bearing whose volume is 9.6 mm3 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? = 1.318… Radius = 1.3 mm (to 2 sf)

10. Hot water tank: Formulae • At the end of the activity The formula for the volume of a tank is V =  r2h 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?

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