© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Hot water tank:

Formulae

These solar panels provide hot water for a house.

V = r2h

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

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

How to work out the volume of the tank…

V = r2h

V = 30 30 150

= 424 115 cm3

1000 cm3 = 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

height150cm

A = r 2

Example Area of a circle with radius 5 cm

5 cm= 5 2

= 78.5398...

Area = 79 cm2 (nearest cm2)

Example Volume of a sphere with radius 5 cm

V = 523.5987...

Volume = 524 cm3 (nearest cm3)

V = r 343

= 5343

Think about…How far should this be rounded?

Think about…How do you work this out on a calculator?

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 cm2 (nearest cm2)Area = 25.68

Think about…What ways could be used to work this out?

S = 2 r (r + h)

radius r

heighth

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 m2 (to nearest m2)

Surface area = 43.228... Think about…How far should this be rounded?

Think about…What ways could you use to work this out?

£P left in building society at r % interest.

Amount after n years:

Example

r100A = P (1 + )n

A = 750 (1 + )6 1004.5

If £750 is invested at 4.5 % interest for 6 years:

= 750 1.0456 = 976.695...

Amount = £976.70 (nearest pence)

Think about…How do you work this out?

Think about…How far should this be rounded?

The radius of a ball bearing whose volume is 9.6 mm3

Radius of sphere

where V is the volume.

Example r = 3V4

3

r = 3 x 9.64

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?

At the end of the activityThe formula for the volume of a tank is V = r2hWhich 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?