Transcript Climate Change - Nuffield Foundation

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 =  r2h
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 =  r2h
V =   30  30  150
diameter 60cm
= 424 115 cm3
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.)
height
150cm
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 cm2 (nearest cm2)
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 cm3 (nearest cm3)
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
4.8 (4.3 + 6.4)
2
Think about…
What ways could be used
to work this out?
Area = 25.68 = 26 cm2 (nearest cm2)
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 m2 (to nearest m2)
Example £P left in building society at r % interest.
Amount after n years:
n
A = P (1 + 100
)
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 3V
4
The radius of a ball bearing whose volume is 9.6 mm3
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 =  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?